Journal Sciences News
Zeitschrift fur Medizinische Physik
May 2018
Optimal insurance design under background risk with dependence
Publication date: May 2018
Source:Insurance: Mathematics and Economics, Volume 80 Author(s): Zhiyi Lu, Shengwang Meng, Leping Liu, Ziqi Han In this paper, we revisit the problem of optimal insurance under a general criterion that preserves stop-loss order when the insured faces two mutually dependent risks: background risk and insurable risk. According to the local monotonicity of conditional survival function, we derive the optimal contract forms in different types of interval. Because the conditional survival function reflects the dependence between background risk and insurable risk, the dependence structure between the two risks plays a critical role in the insured’s optimal insurance design. Furthermore, we obtain the optimal insurance forms explicitly under some special dependence structures. It is shown that deductible insurance is optimal and the Mossin’s Theorem is still valid when background risk is stochastically increasing in insurable risk, which generalizes the corresponding results in Lu et al. (2012). Moreover, we show that an individual will purchase no insurance when the sum of the two risks is stochastically decreasing in insurable risk.
May 2018
On optimal periodic dividend strategies for L
May 2018
Banach Contraction Principle and ruin probabilities in regime-switching models
Publication date: May 2018
Source:Insurance: Mathematics and Economics, Volume 80 Author(s): Les
May 2018
Claims reserving in the presence of excess-of-loss reinsurance using micro models based on aggregate data
Publication date: May 2018
Source:Insurance: Mathematics and Economics, Volume 80 Author(s): Carolin Margraf, Valandis Elpidorou, Richard Verrall This paper addresses a new problem in the literature, which is how to consider reserving issues for a portfolio of general insurance policies when there is excess-of-loss reinsurance. This is very important for pricing considerations and for decision making regarding capital issues. The paper sets out how this is currently often tackled in practice and provides an alternative approach using recent developments in stochastic claims reserving. These alternative approaches are illustrated and compared in an example using real data. The stochastic modelling framework used in this paper is Double Chain Ladder, but other approaches would also be possible. The paper sets out an approach which could be explored further and built on in future research.
May 2018
In memoriam Marc Goovaerts
Publication date: May 2018
Source:Insurance: Mathematics and Economics, Volume 80 Author(s): Rob Kaas, Roger Laeven, Sheldon Lin, Qihe Tang, Gordon Willmot, Hailiang Yang
May 2018
Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility
Publication date: May 2018
Source:Insurance: Mathematics and Economics, Volume 80 Author(s): Pei Wang, Zhongfei Li In this paper, we investigate a robust optimal investment problem for an ambiguity-averse member (AAM) of defined contribution (DC) pension plans with stochastic interest rate and stochastic volatility. The AAM has access to a risk-free asset, a bond and a stock in a financial market. We assume that the interest rate is described by an affine model, which includes the Cox–Ingersoll–Ross model and the Vasicek model as special cases, while the stock price is driven by the Heston’s stochastic volatility model. Moreover, the AAM has different levels of ambiguity aversion about the diffusion parts of the interest rate and the stock’s price and volatility. She attempts to maximize the expected power utility of her terminal wealth under the worst-case scenario. By applying the stochastic dynamic programming approach, we derive a robust optimal investment strategy and the corresponding value function explicitly, and subsequently two special cases are discussed. Finally, a numerical example is presented to illustrate the impact of model parameters on the robust optimal investment strategy and to explain the economic meaning of our theoretical results. The numerical example shows that the AAM’s ambiguity aversion levels about the interest rate and the stock’s price and volatility have different impacts on the proportions invested in the risky assets, and that ignoring model uncertainty always incurs utility losses for the AAM.
May 2018
Large deviations for risk measures in finite mixture models
Publication date: May 2018
Source:Insurance: Mathematics and Economics, Volume 80 Author(s): Valeria Bignozzi, Claudio Macci, Lea Petrella Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is important to investigate the committed error. In this paper we study the asymptotic behaviour of estimated risk measures, as the data sample size tends to infinity, in the fashion of large deviations. We obtain large deviation results by applying the contraction principle, and the rate functions are given by a suitable variational formula; explicit expressions are available for mixtures of two models. Finally, our results are applied to the most common risk measures, namely the quantiles, the Expected Shortfall and the shortfall risk measure.
Available online 14 April 2018
Optimal robust reinsurance-investment strategies for insurers with mean reversion and mispricing
Publication date: May 2018
Source:Insurance: Mathematics and Economics, Volume 80 Author(s): Ailing Gu, Frederi G. Viens, Haixiang Yao This paper considers how to optimize reinsurance and investment decisions for an insurer who has aversion to model ambiguity, who wants to take into consideration time-varying investment conditions via mean reverting models, and who wants to take advantage of statistical arbitrage opportunities afforded by mispricing of stocks. We work under a complex realistic environment: The surplus process is described by a jump–diffusion model and the financial market contains a market index, a risk-free asset, and a pair of mispriced stocks, where the expected return rate of the stocks and the mispricing follow mean reverting stochastic processes which take into account liquidity constraints. The insurer is allowed to purchase reinsurance and to invest in the financial market. We formulate an optimal robust reinsurance-investment problem under the assumption that the insurer is ambiguity-averse to the uncertainty from the financial market and to the uncertainty of the insured’s claims. Ambiguity aversion is an aversion to the uncertainty taken by making investment decisions based on a misspecified model. By employing the dynamic programming approach, we derive explicit formulae for the optimal robust reinsurance-investment strategy and the optimal value function. Numerical examples are presented to illustrate the impact of some parameters on the optimal strategy and on utility loss functions. Among our various practical findings and recommendations, we find that strengthened market liquidity significantly increases the demand for hedging from the mispriced market, to take advantage of the statistical arbitrage it affords.
March 2018
Solvency II, or how to sweep the downside risk under the carpet
Publication date: Available online 14 April 2018
Source:Insurance: Mathematics and Economics Author(s): Stefan Weber Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious deficiency of V@R is that firms can hide their total downside risk in corporate networks, unless a consolidated solvency balance sheet is required for each economic scenario. In this case, they can largely reduce their total capital requirements via appropriate transfer agreements within a network structure consisting of sufficiently many entities and thereby circumvent capital regulation. We prove several versions of such a result for general distortion risk measures of V@R-type, explicitly construct suitable allocations of the network portfolio, and finally demonstrate how these findings can be extended beyond distortion risk measures. We also discuss why consolidation requirements cannot completely eliminate this problem. Capital regulation should thus be based on coherent or convex risk measures like average value at risk or expectiles.
March 2018
Editorial Board
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79

March 2018
Pricing insurance drawdown-type contracts with underlying L
March 2018
Insurance loss coverage and demand elasticities
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): MingJie Hao, Angus S. Macdonald, Pradip Tapadar, R. Guy Thomas Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome. We suggest a counter-argument to this perception in circumstances where modest levels of adverse selection lead to an increase in ‘loss coverage’, defined as expected losses compensated by insurance for the whole population. This happens if the shift in coverage towards higher risks under adverse selection more than offsets the fall in number of individuals insured. The possibility of this outcome depends on insurance demand elasticities for higher and lower risks. We state elasticity conditions which ensure that for any downward-sloping insurance demand functions, loss coverage when all risks are pooled at a common price is higher than under fully risk-differentiated prices. Empirical evidence suggests that these conditions may be realistic for some insurance markets.
March 2018
An IBNR–RBNS insurance risk model with marked Poisson arrivals
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Soohan Ahn, Andrei L. Badescu, Eric C.K. Cheung, Jeong-Rae Kim Inspired by the claim reserving problem in non-life insurance, this paper proposes to study the insurer’s surplus process under a micro-level framework, with particular focus on modeling the Incurred But Not Reported (IBNR) and the Reported But Not Settled (RBNS) claims. It is assumed that accidents occur according to a Poisson point process, and each accident is accompanied by a claim developmental mark that contains the reporting time, the settlement time, and the size of (possibly multiple) payments between these two times. Under exponential reporting and settlement delays, we show that our model can be represented as a Markovian risk process with countably infinite number of states. This can in turn be transformed to an equivalent fluid flow model when the payments are phase-type distributed. As a result, classical measures such as ruin probability or more generally the Gerber–Shiu expected discounted penalty function follow directly. The joint Laplace transform and the pairwise joint moments involving the ruin time and the aggregate payments of different types (with and without claim settlement) are further derived. Numerical illustrations are given at the end, including the use of a real insurance dataset.
March 2018
Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Boda Kang, Jonathan Ziveyi In this paper we analyse how the policyholders’surrender behaviour is influenced by changes in various sources of risk impacting a variable annuity (VA) contract embedded with a guaranteed minimum maturity benefit rider that can be surrendered anytime prior to maturity. We model the underlying mutual fund dynamics by combining a Heston (1993) stochastic volatility model together with a Hull and White (1990) stochastic interest rate process. The model is able to capture the smile/skew often observed on equity option markets (Grzelak and Oosterlee 2011) as well as the influence of the interest rates on the early surrender decisions as noted from our analysis. The annuity provider charges management fees which are proportional to the level of the mutual fund as a way of funding the VA contract. To determine the optimal surrender decisions, we present the problem as a 4-dimensional free-boundary partial differential equation (PDE) which is then solved efficiently by the method of lines (MOL) approach. The MOL algorithm facilitates simultaneous computation of the prices, fair management fees, optimal surrender boundaries and hedge ratios of the variable annuity contract as part of the solution at no additional computational cost. A comprehensive analysis on the impact of various risk factors in influencing the policyholder’s surrender behaviour is carried out, highlighting the significance of both stochastic volatility and interest rate parameters in influencing the policyholder’s surrender behaviour. With the aid of the hedge ratios obtained from the MOL, we construct an effective dynamic hedging strategy to mitigate the provider’s risk and compare different hedging performances when the policyholders’ surrender behaviour is either optimal or sub-optimal.
March 2018
A time of ruin constrained optimal dividend problem for spectrally one-sided L
March 2018
Ruin probability via Quantum Mechanics Approach
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Muhsin Tamturk, Sergey Utev The finite time ruin probability in the classical surplus process setup with additional capital injections and withdrawals is investigated via the Quantum Mechanics Approach. The results are compared with the Picard–Lefevre Appell Polynomial approach and the traditional Markov Chain approach. In addition, several optimization problems in the insurance market are numerically solved by applying the Quantum Mechanics Approach.
March 2018
Weighted risk capital allocations in the presence of systematic risk
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Edward Furman, Alexey Kuznetsov, Ri
March 2018
Distortion measures and homogeneous financial derivatives
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): John A. Major This paper extends the evaluation and allocation of distortion risk measures to apply to arbitrary homogeneous operators (“financial derivatives,” e.g. reinsurance recovery) of primitive portfolio elements (e.g. line of business losses). Previous literature argues that the allocation of the portfolio measure to the financial derivative should take the usual special-case form of Aumann–Shapley, being a distortion-weighted “co-measure” expectation. This is taken here as the definition of the “distorted” measure of the derivative “with respect to” the underlying portfolio. Due to homogeneity, the subsequent allocation of the derivative’s value to the primitive elements of the portfolio again follows Aumann–Shapley, in the form of the exposure gradient of the distorted measure. However, the gradient in this case is seen to consist of two terms. The first is the familiar distorted expectation of the gradient of the financial derivative with respect to exposure to the element. The second term involves the conditional covariance of the financial derivative with the element. Sufficient conditions for this second term to vanish are provided. A method for estimating the second term in a simulation framework is proposed. Examples are provided.
March 2018
An approximation method for risk aggregations and capital allocation rules based on additive risk factor models
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Ming Zhou, Jan Dhaene, Jing Yao This paper proposes the use of convex lower bounds as approximation to evaluate the aggregation of risks, based on additive risk factor models in the multivariate generalized Gamma distribution context. We consider two types of additive risk factor model. In Model 1, the risk factors that contribute to the aggregation are deterministic. In Model 2, we consider contingent risk factors. We work out the explicit formulae of the convex lower bounds, by which we propose an analytical approximate capital allocation rule based on the conditional tail expectation. We conduct stress tests to show that our method is robust across various dependence structures.
March 2018
Using fuzzy logic to interpret dependent risks
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Sibel Acik Kemaloglu, Arnold F. Shapiro, Fatih Tank, Aysen Apaydin One reason why an independent claim amounts assumption underlies classic risk models is because it simplifies calculations. As an alternative, this paper investigates the dependence structure via the Farlie–Gumbel–Morgenstern (FGM) Copula and its interpretation given a fuzzy logic approach for claim amounts arising from a Pareto distribution.
March 2018
Robust evaluation of SCR for participating life insurances under Solvency II
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Donatien Hainaut, Pierre Devolder, Antoon Pelsser This article proposes a robust framework to evaluate the solvency capital requirement (SCR) of a participating life insurance with death benefits. The preference for robustness arises from the ambiguity caused by the market incompleteness, model shortcomings and parameters misspecifications. To incorporate the uncertainty in the procedure of evaluation, we consider a set of potential equivalent pricing measures in the neighborhood of the real one. In this framework, closed form expressions for the net asset value (NAV) and for its moments are found. The SCR is next approximated by the Value at Risk of Gaussian or normal inverse Gaussian (NIG) random variables, approaching the NAV distribution and fitted by moments matching.
March 2018
De-risking strategy: Longevity spread buy-in
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Valeria D’Amato, Emilia Di Lorenzo, Steven Haberman, Pretty Sagoo, Marilena Sibillo The paper proposes a demographic de-risking strategy for a pension provider, to deal with the future uncertainty in longevity over a long time horizon. The innovative idea of a longevity spread buy-in is presented. The formulae for calculating the buy-in premium are proposed in the case of pension plans. The proposal directly impacts the pension provider’s risk management systems and hence can be an important part of the overall approach to risk management. The numerical results, developed under specified stochastic hypotheses for the dynamics of the underlying financial and demographic processes, show how the proposal of the paper can be practically implemented.
March 2018
Expected utility of the drawdown-based regime-switching risk model with state-dependent termination
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): David Landriault, Bin Li, Shu Li In this paper, we model an entity’s surplus process X using the drawdown-based regime-switching (DBRS) dynamics proposed in Landriault et al. (2015a). We introduce the state-dependent termination time to the model, and provide rationale for its introduction in insurance contexts. By examining some related potential measures, we first derive an explicit expression for the expected terminal utility of the entity in the DBRS model with Brownian motion dynamics. The analysis is later generalized to time-homogeneous Markov framework, where the spectrally negative L
March 2018
Stochastic distortion and its transformed copula
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Feng Lin, Liang Peng, Jiehua Xie, Jingping Yang Motivated by wide applications of distortion functions and copulas in insurance and finance, this paper generalizes the notion of a deterministic distortion function to a stochastic distortion, i.e., a random process, and employs the defined stochastic distortion to construct a so-called transformed copula by stochastic distortions. One method for constructing stochastic distortions is provided with a focus on using time-changed processes. After giving some families of the transformed copulas by stochastic distortions, a particular class of transformed copulas is applied to a portfolio credit risk model, where a numeric study shows the advantage of using the transformed copulas over the conventional Gaussian copula and the double t copula in terms of the fitting accuracy and the ability of catching tail dependence.
March 2018
Annuitization and asset allocation under exponential utility
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Xiaoqing Liang, Virginia R. Young We find the optimal investment, consumption, and annuitization strategies for a retiree who wishes to maximize her expected discounted utility of lifetime consumption. We assume that the retiree’s preferences exhibit constant absolute risk aversion (CARA), that is, the retiree’s utility function is exponential. The retiree invests in a financial market with one riskless and one risky asset, the so-called Black–Scholes market. Moreover, the retiree may purchase single-premium immediate life annuity income that is payable continuously, and she may purchase this life annuity income at any time and for any amount, subject to the limit of her available wealth. Because maximizing exponential utility generally does not prevent wealth from dropping below 0, we restrict the investment, consumption, and annuitization strategies so that wealth remains non-negative. We solve the optimization problem via stochastic control and obtain semi-explicit solutions by using the Legendre dual. We prove that the optimal annuitization strategy is a barrier strategy. We also provide some numerical examples to illustrate our results and to analyze their sensitivity to the parameters.
March 2018
On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Raluca Vernic In this paper, we consider Sarmanov’s multivariate discrete distribution as counting distribution in two multivariate compound models: the first model assumes different types of independent claim sizes (corresponding to, e.g., different types of insurance policies), while in the second model, we introduce some dependency between the claims (motivated by the events that can simultaneously affect several types of policies). Since Sarmanov’s distribution can join different types of marginals, we also assume that these marginals belong to Panjer’s class of distributions and discuss the evaluation of the resulting compound distribution based on recursions. Alternatively, the evaluation of the same distribution using the Fast Fourier Transform method is also presented, with the purpose to significantly reduce the computing time, especially in the dependency case. Both methods are numerically illustrated and compared from the point of view of speed and accuracy.
March 2018
Optimal investment under VaR-Regulation and Minimum Insurance
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): An Chen, Thai Nguyen, Mitja Stadje We look at an optimal investment problem of a financial institution operating under a joint Value-at-Risk and a portfolio insurance constraint. This analysis is particularly relevant for an insurance company operating under the Solvency II regulation which aims to maximize the expected utility of its shareholders, while at the same time being required to provide its policyholders a minimum guaranteed amount. Using static Lagrangian method, we solve the pointwise utility optimization problem to achieve the global maximum by carefully comparing the local maximizers with the jump point or the boundary. Our theoretical and numerical results show that contrary to a pure Value-at-Risk regulation, an insurance company that operates not only under a Solvency II VaR constraint but additionally has to serve a minimal guarantee admits a comprehensive but not too costly protection, and at the same time displays prudent investment behavior. This result holds for both constant and stochastic volatility settings.
March 2018
Optimal investment management for a defined contribution pension fund under imperfect information
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Ling Zhang, Hao Zhang, Haixiang Yao This paper investigates an optimal multi-period investment management problem for a defined contribution pension fund under the mean–variance criterion with imperfect information, meaning that both observable and unobservable states exist in the financial market. The dynamics of the unobservable market state process are formulated by a discrete-time finite-state hidden Markov chain with time-varying transition probability matrices. Due to the long investment horizon of a defined contribution pension fund, our paper considers only risky assets whose returns depend on both the observable and unobservable market states. Meanwhile, the stochastic salary process is also modulated by the observable and unobservable market states. By adopting sufficient statistics, the portfolio optimization problem for the defined contribution pension fund with imperfect information is transformed into one with complete information. Then, the optimal investment strategy and the efficient frontier are explicitly derived using the dynamic programming approach and the Lagrange dual method. Finally, numerical results show that the imperfection of market state information may cause a loss of investment return.
March 2018
Optimal dividends under Erlang(2) inter-dividend decision times
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Benjamin Avanzi, Vincent Tu, Bernard Wong In the classical dividends problem, dividend decisions are allowed to be made at any time. Under such a framework, the optimal dividend strategies are often of barrier or threshold type, which can lead to very irregular dividend payments over time. In practice however companies distribute dividends on a periodic basis. In that spirit, “Erlangisation” techniques have been used to approximate problems with fixed inter-dividend decision times. When studying the optimality of such strategies, the existing literature focuses exclusively on the special case of exponential – that is, Erlang(1) – inter-dividend decision times. Higher dimensional models are surprisingly difficult to study due to the implicit nature of some of the equations. While some of this difficulty continues to exist in high dimensions, in this paper we provide a stepping stone to the general Erlang( n ) problem by providing a detailed analysis of the optimality of periodic barrier strategies when inter-dividend-decision times are Erlang(2) distributed. Results are illustrated.
March 2018
On existence and uniqueness of the principle of equivalent utility under Cumulative Prospect Theory
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): J. Chudziak We establish a necessary and sufficient condition for the existence and uniqueness of the principle of equivalent utility under Cumulative Prospect Theory.
Available online 27 February 2018
On generalized log-Moyal distribution: A new heavy tailed size distribution
Publication date: March 2018
Source:Insurance: Mathematics and Economics, Volume 79 Author(s): Deepesh Bhati, Sreenivasan Ravi A new class of distributions, the generalized log-Moyal, suitable for modelling heavy tailed data is proposed in this article. This class exhibits desirable properties relevant to actuarial science and inference. The proposed distribution can be related to some well known distributions like Moyal, folded-normal and chi-square. Statistical inference of the model parameters is discussed using the method of quantiles and the method of maximum likelihood estimation. Three celebrated data sets, namely, Norwegian fire insurance losses, Danish fire insurance losses and vehicle insurance losses, are used to show the applicability of the new class of distributions. Parametric regression modelling is discussed assuming that the response variable follows the generalized log-Moyal distribution.
Available online 10 January 2018
Optimal investment strategies and intergenerational risk sharing for target benefit pension plans
Publication date: Available online 27 February 2018
Source:Insurance: Mathematics and Economics Author(s): Suxin Wang, Yi Lu, Barbara Sanders In this paper, we consider a stochastic model for a target benefit pension fund in continuous time, where the plan members’ contributions are set in advance while the pension payments depend on the financial situation of the plan, with risk sharing between different generations. The pension fund is invested in both a risk-free asset and a risky asset. In particular, stochastic salary rates and the correlation between salary movements and financial market fluctuations are considered. Using the stochastic optimal control approach, we derive closed-form solutions for optimal investment strategies as well as optimal benefit payment adjustments, which minimize the combination of benefit risk (in terms of deviating from the target) and intergenerational transfers. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and salary rates. We also consider how the optimal benefit changes with respect to different target levels.
January 2018
Life insurance settlement and the monopolistic insurance market
Publication date: Available online 10 January 2018
Source:Insurance: Mathematics and Economics Author(s): Jimin Hong, S. Hun Seog We analyze the effects of life insurance settlement on insurance contract design, the insurer’s profit and welfare. Policyholders face not only mortality risks but also heterogeneous liquidity risks which lead the policyholders to surrender or settle the policies. It is assumed that the insurer cannot discriminate policyholders based on liquidity risks, and that no cost is incurred in surrender and settlement. We characterize the conditions for the endogenous existence of a settlement market, and find that the settlement market, if it exists, raises insurance premium. The effects of settlement on profit and welfare depend on the market structure. In the monopolistic insurance market, the settlement market lowers the insurer’s profit, and consumer welfare increases whenever demand increases and possibly increases even when demand decreases. This finding is in contrast with most of the existing studies reporting that settlement never has a positive effect on welfare. In the competitive insurance market, welfare always decreases.
January 2018
Editorial Board
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78

January 2018
IME’s Editorial Board
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Rob Kaas, Roger Laeven, Sheldon Lin, Qihe Tang, Gordon Willmot, Hailiang Yang As of 2018, IME will have a new set of editors. This editorial describes the current and future state-of-affairs.
January 2018
Longevity risk and capital markets: The 2015–16 update
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): David Blake, Nicole El Karoui, St
January 2018
The choice of trigger in an insurance linked security: The mortality risk case
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Richard MacMinn, Andreas Richter In 2003, Swiss Re introduced a mortality-based security designed to hedge excessive mortality changes for its life book of business. The concern was mortality risk, i.e., the risk of premature death. The mortality risk due to a pandemic is similar to the property risk associated with catastrophic events such as earthquakes and hurricanes and the security used to hedge the risk is similar to a CAT bond. This work looks at the incentives associated with insurance linked securities. It considers the trade-offs an insurer or reinsurer faces in selecting a hedging strategy. We compare index and indemnity-based hedging as alternative design choices and ask which is capable of creating the greater value for stakeholders. Additionally, we model an insurer or reinsurer that is subject to insolvency risk, which creates an incentive problem known as the judgment proof problem. The corporate manager is assumed to act in the interests of shareholders and so the judgment proof problem yields a conflict of interest between shareholders and other stakeholders. Given the fact that hedging may improve the situation, the analysis addresses what type of hedging tool would be best. We show that an indemnity-based security tends to worsen the situation, as it introduces an additional incentive problem. Index-based hedging, on the other hand, under certain conditions turns out to be beneficial and therefore dominates indemnity-based strategies. This result is further supported by showing that for the same sufficiently small strike price the current shareholder value is greater with the index-based security than the indemnity-based security.
January 2018
Pension risk management with funding and buyout options
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Samuel H. Cox, Yijia Lin, Tianxiang Shi There has been a surge of interest in recent years from defined benefit pension plan sponsors in de-risking their plans with strategies such as “longevity hedges” and “pension buyouts” (Lin et al., 2015). While buyouts are attractive in terms of value creation, they are capital intensive and expensive, particularly for firms with underfunded plans. The existing literature mainly focuses on the costs and benefits of pension buyouts. Little attention has been paid to how to capture the benefits of de-risking within a plan’s financial means, especially when buyout deficits are significant. To fill this gap, we propose two options, namely a pension funding option and pension buyout option, that provide financing for both underfunded and well funded plans to cover the buyout risk premium and the pension funding deficit, if a certain threshold is reached. To increase market liquidity, we create a transparent pension funding index, calculated from observed capital market indices and publicly available mortality tables as well as pension mandatory contributions, to determine option payoffs. A simulation based pricing framework is then introduced to determine the prices of the proposed pension options. Our numerical examples show that these options are effective and economically affordable. Moreover, our sensitivity analyses demonstrate the reliability of our pricing models.
January 2018
The effect of longevity drift and investment volatility on income sufficiency in retirement
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Les Mayhew, David Smith, Douglas Wright In 2014 the Government announced radical proposals which now allow people to withdraw money from their pension pot from age 55, ‘how they want, subject to their marginal rate of income tax in that year’. The main effect of this change will be to put more onus on the individual to make sure they have sufficient resources to last for their retirement, but it also removes the obligation to annuitise their funds at any future age. This paper is concerned with how people can best use their pension pots by aligning them to their personal financial objectives and longevity risks. It finds that for most people annuitising is not the best option, except for a few circumstances, and that draw down is preferable, especially where there is a bequest motive and the individual has assets such as property to fall back on. These options are low risk if simple rules are followed but they are not a substitute for professional advice and should only be used in conjunction.
January 2018
Valuation of longevity-linked life annuities
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Jorge Miguel Bravo, Najat El Mekkaoui de Freitas In this paper we show that the fair value of a pure longevity-linked life annuity can be decomposed into a traditional fixed annuity and a basket of European-style longevity (call and put) options of different maturities with underlying asset equal to a longevity-index and strike equal to the minimum (initial) guaranteed amount. The embedded longevity put (call) options give the annuity provider (annuitant) the right to periodically adjust the benefit payments downwards (upwards) if the observed survivorship rates are higher (lower) than those predicted at the contract initiation, transferring part of the longevity risk to the annuitant. Alternative decompositions for the payout stream of a capped longevity-linked life annuity are also explored. We incorporate capital market risk and assess how individuals with different risk aversion and subjective time preferences value the stochastic payout stream of both index-linked and participating contract structures. We discuss the valuation of the embedded longevity options using a risk-neutral simulation approach. The paper revisits and expands previous results on the problem of designing and pricing life annuity contracts which aim at sharing longevity and investment risk between annuity provider and annuitants within the context of building the post-retirement income.
January 2018
Unisex pricing of German participating life annuities—Boon or bane for customer and insurance company?
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Sandy Bruszas, Barbara Kasch
January 2018
Valuation of variable long-term care Annuities with Guaranteed Lifetime Withdrawal Benefits: A variance reduction approach
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Ming-hua Hsieh, Jennifer L. Wang, Yu-Fen Chiu, Yen-Chih Chen This paper proposes a new product, the Variable Life Care Annuity with Guaranteed Lifetime Withdrawal Benefits (LCA-GLWB), and designs an efficient valuation algorithm. This innovative product provides a comprehensive retirement solution for both longevity risk and long-term care protection. It includes the benefits of guaranteed income streams with downside risk protection and long-term care expenses for retirees. However, the valuation of this type of product is both complex and time-consuming. In this paper, we propose a Monte Carlo valuation algorithm that uses the variance reduction technique. The numerical results indicate that the proposed valuation algorithm is very efficient under a broad range of asset return models. The proposed algorithm provides a general approach for the rapid valuation of similar products and can help provide life insurance companies offering innovative products with an appropriate valuation tool.
January 2018
Profitability and risk profile of reverse mortgages: A cross-system and cross-plan comparison
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Yung-Tsung Lee, Ko-Lun Kung, I-Chien Liu This study conducts a cross-system and cross-plan comparison of reverse mortgages. We compare the systematic distinctions and analyze the risk and profitability of reverse mortgages in two prominent types of market arrangements: (1) A market where a public external insurer exists (i.e., the Home Equity Conversion Mortgage program in the U.S. market). (2) A market where an external insurer is absent (i.e., the Australian market). Two typical payment plans, the lump-sum and annuity payment, are examined and compared using stochastic dominance criteria. This paper provides a complete framework to analyze the profitability and risk profile of reverse mortgage products, particularly the stochastic dominance criteria. This study argues that the modern solvency capital requirement such as Solvency II may depress the loan-to-value ratio and the intervention of government may be necessary. We also demonstrate that the lender prefers the lump-sum products and this may explain why the lump-sum products dominate the market in practice. Our work can help financial institutions and governments understand the properties of reverse mortgages, and provides a necessary incentive for these organizations to develop a reverse mortgage market.
January 2018
A strategy for hedging risks associated with period and cohort effects using q-forwards
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Yanxin Liu, Johnny Siu-Hang Li The stochastic nature of future mortality arises from both period (time-related) and cohort (year-of-birth-related) effects. Existing index-based longevity hedging strategies mitigate the risk associated with period effects, but often overlook cohort effects. The negligence of cohort effects may lead to sub-optimal hedge effectiveness, if the liability being hedged is a deferred pension or annuity which involves cohorts that are not covered by the data sample. In this paper, we propose a new hedging strategy that incorporates both period and cohort effects. The resulting longevity hedge is a value hedge, reducing the uncertainty surrounding the
January 2018
Replicating intergenerational longevity risk sharing in collective defined contribution pension plans using financial markets
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Enareta Kurtbegu Intergenerational risk sharing is often seen as a strong point of the Dutch pension system. The ability to absorb financial and actuarial shocks through the funding ratio allows for the smoothing of returns over generations. Nevertheless, it implicitly means that generations subsidize each other, which has its disadvantages, especially in the light of incomplete contracts and situations of hard regulation constraints. This paper highlights the advantages of intergenerational risk sharing as a main characteristic in certain collective pension plans, investigating if and how much of this can be replicated by individual participation in the market. Using a stylized model based on different pension plans such as “hard”/“soft” defined benefit, collective/“pure” defined contribution, this paper identifies the effects of an increase in life-expectancy as one of the most important actual demographic shocks. The existence of regulatory constraints modifies agents’ behavior so that they tend to choose individual investment to ensure their retirement savings. In the absence of regulatory constraints, individual investment under-performs and highly replicates pension fund performance. Thus, choosing collective participation is more rational. Moreover, as the effect of the shock is decomposed, a discussion of the absorption heterogeneity by different plans is presented.
January 2018
Cause-of-death mortality: What can be learned from population dynamics?
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Alexandre Boumezoued, H
January 2018
Using Taiwan National Health Insurance Database to model cancer incidence and mortality rates
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Jack C. Yue, Hsin-Chung Wang, Yin-Yee Leong, Wei-Ping Su The increasing cancer incidence and decreasing mortality rates in Taiwan worsened the loss ratio of cancer insurance products and created a financial crisis for insurers. In general, the loss ratio of long-term health products seems to increase with the policy year. In the present study, we used the data from Taiwan National Health Insurance Research Database to evaluate the challenge of designing cancer products. We found that the Lee–Carter and APC models have the smallest estimation errors, and the CBD and Gompertz models are good alternatives to explore the trend of cancer incidence and mortality rates, especially for the elderly people. The loss ratio of Taiwan’s cancer products is to grow and this can be deemed as a form of longevity risk. The longevity risk of health products is necessary to face in the future, similar to the annuity products.
January 2018
Do actuaries believe in longevity deceleration?
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Edouard Debonneuil, St
January 2018
The double-gap life expectancy forecasting model
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Marius D. Pascariu, Vladimir Canudas-Romo, James W. Vaupel Life expectancy is highly correlated over time among countries and between males and females. These associations can be used to improve forecasts. Here we propose a method for forecasting female life expectancy based on analysis of the gap between female life expectancy in a country compared with the record level of female life expectancy in the world. Second, to forecast male life expectancy, the gap between male life expectancy and female life expectancy in a country is analysed. We present these results for various developed countries. We compare our results with forecasts based on the Lee–Carter approach and the Cairns–Blake–Dowd strategy. We focus on forecasting life expectancy at age 0 and remaining life expectancy at age 65.

Mortality models and longevity risk for small populations
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Hsin-Chung Wang, Ching-Syang Jack Yue, Chen-Tai Chong Prolonging life expectancy and improving mortality rates is a common trend of the 21 st century. Stochastic models, such as Lee–Carter model (Lee and Carter, 1992), are a popular choice to deal with longevity risk. However, these mortality models often have unsatisfactory results for the case of small populations. Thus, quite a few modifications (such as approximation and maximal likelihood estimation) to the Lee–Carter can be used for the case of small populations or missing observations. In this study, we propose an alternative approach (graduation methods) to improve the performance of stochastic models. The proposed approach is a combination of data aggregation and mortality graduation. In specific, we first combine the historical data of target population, treating it as the reference population, and use the data graduation methods (Whittaker and partial standard mortality ratio) to stabilize the mortality estimates of the target population. We first evaluate whether the proposed method have smaller errors in mortality estimation than the Lee–Carter model in the case of small populations, and explore if it is possible to reduce the bias of parameter estimates in the Lee–Carter model. We found that the proposed approach can improve the model fit of the Lee–Carter model when the population size is 200,000 or less.
view: 147

$2 OFF $19, $4 OFF $39, $6 OFF $59, $8 OFF $79, offer valid until 04/30/2018.

Code: SHOPTG2

Start: 29 Oct 2017 | End: 30 Apr 2018

ULTIMATE SUPERFOOD BLEND Packed with Seeds, Fruits & Vegetables

Start: 07 Nov 2017 | End: 07 May 2018

Shop for Decorative pillows starting at $21 at domino!

Start: 17 Sep 2017 | End: 30 Apr 2018

Search All Amazon* UK* DE* FR* JP* CA* CN* IT* ES* IN* BR* MX
Booking.com B.V. is based in Amsterdam in the Netherlands. Ready for some statistics? Our 1,534,024 properties, including 860,482 holiday rentals, are located in 123,105 destinations in 229 countries and territories, and are supported internationally by 198 offices in 70 countries.
2013 Copyright © Techhap.com Mobile version 2015 | PeterLife & company
Skimlinks helps publishers monetize editorial content through automated affiliate links for products.
Terms of use Link at is mandatory if site materials are using fully or particulary.
Were treated to the site administrator, a cup of coffee *https://paypal.me/peterlife
Yandex.ru