Journal Sciences News
Zeitschrift fur Medizinische Physik
Available online 4 January 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.
January 2018
Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates
Publication date: Available online 4 January 2018
Source:Insurance: Mathematics and Economics Author(s): Boda Kang, Jonathan Ziveyi In this paper we analyse how the policyholder 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.
January 2018
An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Yixing Zhao, Rogemar Mamon We introduce a pricing framework for a guaranteed annuity option (GAO) where both the interest and mortality risks are correlated. We assume that the short rate and the force of mortality follow the Cox–Ingersoll–Ross (CIR) and Lee–Carter models, respectively. Employing the change of measure technique, we decompose the pure endowment into the product of the bond price and survival probability, thereby facilitating the evaluation of the annuity expression. With the aid of the dynamics of interest and mortality processes under the forward measure, we construct an algorithm based on comonotonicity theory to estimate the quantiles of survival probability and annuity rate. The comonotonic upper and lower bounds in the convex order are used to approximate the annuity and GAO prices and henceforth avoiding the simulation-within-simulation problem. Numerical illustrations show that our algorithm gives an efficient and practical method to estimate GAO values.
January 2018
From Concentration Profiles to Concentration Maps. New tools for the study of loss distributions
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Andrea Fontanari, Pasquale Cirillo, Cornelis W. Oosterlee We introduce a novel approach to risk management, based on the study of concentration measures of the loss distribution. We show that indices like the Gini index, especially when restricted to the tails by conditioning and truncation, give us an accurate way of assessing the variability of the larger losses – the most relevant ones – and the reliability of common risk management measures like the Expected Shortfall. We first present the Concentration Profile, which is formed by a sequence of truncated Gini indices, to characterize the loss distribution, providing interesting information about tail risk. By combining Concentration Profiles and standard results from utility theory, we develop the Concentration Map, which can be used to assess the risk attached to potential losses on the basis of the risk profile of a user, her beliefs and historical data. Finally, with a sequence of truncated Gini indices as weights for the Expected Shortfall, we define the Concentration Adjusted Expected Shortfall, a measure able to capture additional features of tail risk. Empirical examples and codes for the computation of all the tools are provided.
January 2018
Early default risk and surrender risk: Impacts on participating life insurance policies
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Chunli Cheng, Jing Li We study the risk-neutral valuation of participating life insurance policies with surrender guarantees when an early default mechanism, forcing an insurance company to be liquidated once a solvency threshold is reached, is imposed by a regulator. The early default regulation affects the policies’ value not only directly via changing the policies’ payment stream but also indirectly via influencing policyholder’s surrender. In this paper, we endogenize surrender risk by assuming a representative policyholder’s surrender intensity bounded from below and from above and uncover the impact of the regulation on the policyholder’s surrender decision making. A partial differential equation is derived to characterize the price of a participating policy and solved with the finite difference method. We discuss the impacts of the early default regulation and insurance company’s reaction to the regulation in terms of its investment strategy on the policyholder’s surrender as well as on the contract value, which depend on the policyholder’s rationality level.
January 2018
Duality in ruin problems for ordered risk models
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Pierre-Olivier Goffard, Claude Lef
January 2018
Dependent risk models with Archimedean copulas: A computational strategy based on common mixtures and applications
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): H
January 2018
Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Danping Li, Yang Shen, Yan Zeng This paper considers the derivative-based optimal investment strategies for an asset–liability management (ALM) problem under the mean–variance criterion in the presence of stochastic volatility. Specifically, an asset–liability manager is allowed to invest not only in a risk-free bond and a stock, but also in a derivative, whose price depends on the underlying price of the stock and its volatility. By solving a system of two backward stochastic differential equations, we derive the explicit expressions of the efficient strategies and the corresponding efficient frontiers in two cases, with and without the derivative asset. Moreover, we consider the special case of an optimal investment problem with no liability commitment, which is also not studied in the literature. We also provide some numerical examples to illustrate our results and find that the efficient frontier of the case with the derivative is always better than that of the case without the derivative. Moreover, under the same variance, the expectation of the case with the derivative can reach up to as twice as that of the case without the derivative in some situations.
January 2018
Asset allocation for a DC pension fund under stochastic interest rates and inflation-protected guarantee
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Mei-Ling Tang, Son-Nan Chen, Gene C. Lai, Ting-Pin Wu This paper aims to propose referable asset allocation criteria for a defined-contribution (DC) pension plan under stochastic interest rates and the minimum guarantee of inflation protection on annuities. Motivated by the work of Litterman and Scheinkman (1991), which verifies that interest rate risks could be properly modeled with multiple factors, our proposed model extends the Jarrow and Yildirim (JY, 2003) model to a multi-factor framework, and simultaneously incorporates a stock asset to develop what is called the extended JY model in this study. The extended JY model can specify an economic environment with the consideration of risks arising from nominal and real interest rates, the CPI index (inflation rates), and the value of a stock portfolio, which facilitates to complete the closed-form solutions for the stochastic dynamic programming problem of a DC pension plan. The subsequent numerical experiment examines the allocative behaviors in an inflationary economy. In addition, the term effects among interest rates show to have a substantial impact on allocative decisions, and thus can be properly exploited to improve the final wealth of the pension fund.
January 2018
Stochastic orders and co-risk measures under positive dependence
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): M.A. Sordo, A.J. Bello, A. Su
January 2018
Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): J. Beirlant, G. Maribe, A. Verster The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value index can be substantial and depends strongly on the amount of censoring. We review the available estimators, propose a new bias reduced estimator, and show how shrinkage estimation can help to keep the MSE under control. A bootstrap algorithm is proposed to construct confidence intervals. We compare these new proposals with the existing estimators through simulation. We conclude this paper with a detailed study of a long-tailed car insurance portfolio, which typically exhibits heavy censoring.
January 2018
Non-cooperative dynamic games for general insurance markets
Publication date: January 2018
Available online 1 January 2018
Approximation of ruin probabilities via Erlangized scale mixtures
Publication date: January 2018
Source:Insurance: Mathematics and Economics, Volume 78 Author(s): Oscar Peralta, Leonardo Rojas-Nandayapa, Wangyue Xie, Hui Yao In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cram
Available online 28 December 2017
A time of ruin constrained optimal dividend problem for spectrally one-sided L
Available online 24 December 2017
Weighted risk capital allocations in the presence of systematic risk
Publication date: Available online 28 December 2017
Source:Insurance: Mathematics and Economics Author(s): Edward Furman, Alexey Kuznetsov, Ri
Available online 21 December 2017
Ruin probability via Quantum Mechanics Approach
Publication date: Available online 24 December 2017
Source:Insurance: Mathematics and Economics 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.
Available online 21 December 2017
Expected utility of the drawdown-based regime-switching risk model with state-dependent termination
Publication date: Available online 21 December 2017
Source:Insurance: Mathematics and Economics 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 (2015). 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
Available online 15 December 2017
An IBNR-RBNS insurance risk model with marked Poisson arrivals
Publication date: Available online 21 December 2017
Source:Insurance: Mathematics and Economics 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 modelling 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.
Available online 7 November 2017
Distortion measures and homogeneous financial derivatives
Publication date: Available online 15 December 2017
Source:Insurance: Mathematics and Economics 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.
Available online 6 November 2017
Quantitative assessment of common practice procedures in the fair evaluation of embedded options in insurance contracts
Publication date: Available online 7 November 2017
Source:Insurance: Mathematics and Economics Author(s): Anna Maria Gambaro, Riccardo Casalini, Gianluca Fusai, Alessandro Ghilarducci This work analyses the common industry practice used to evaluate financial options written on with-profit policies issued by European insurance companies. In the last years regulators introduced, with the Solvency II directive, a market consistent valuation framework for determining the fair value of asset and liabilities of insurance funds. A relevant aspect is how to deal with the estimation of sovereign credit and liquidity risk, that are important components in the valuation of the majority of insurance funds, which are usually heavily invested in treasury bonds. The common practice is the adoption of the certainty equivalent approach (CEQ) for the risk neutral evaluation of insurance liabilities, which results in a deterministic risk adjustment of the securities cash flows. In this paper, we propose an arbitrage free stochastic model for interest rate, credit and liquidity risks, that takes into account the dependences between different government bond issuers. We test the impact of the common practice against our proposed model, via Monte Carlo simulations. We conclude that in the estimation of options whose pay-off is determined by statutory accounting rules, which is often the case for European traditional with-profit insurance products, the deterministic adjustment for risk of the securities cash flows is not appropriate, and that a more complete model such as the one described in this article is a viable and sensible alternative in the context of market consistent evaluations.
November 2017
Discounted penalty function at Parisian ruin for L
November 2017
Editorial Board
Publication date: November 2017
Source:Insurance: Mathematics and Economics, Volume 77

November 2017
Wanting robustness in insurance: A model of catastrophe risk pricing and its empirical test
Publication date: November 2017
Source:Insurance: Mathematics and Economics, Volume 77 Author(s): Wenge Zhu Motivated by the fact that a lack of information about natural disasters may lead agents to be ambiguity averse to catastrophe risks, we introduce a new type of penalty function and propose an adjusted equilibrium model based on the function by allowing agents to act in a robust control framework against model misspecification with respect to rare events. The pricing formulas are then derived for various catastrophe linked securities such as catastrophe futures, options and bonds. We also estimate and test the model using empirical data of catastrophe bonds and compare it with various other models and investigate the robustness performance of alternative pricing formulas.
November 2017
Pareto-optimal reinsurance arrangements under general model settings
Publication date: November 2017
Source:Insurance: Mathematics and Economics, Volume 77 Author(s): Jun Cai, Haiyan Liu, Ruodu Wang In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. For the purpose of practice, we use numerical examples to show how to determine the mutually acceptable Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer’s aim and the reinsurer’s goal can be met under the mutually acceptable Pareto-optimal reinsurance contracts.
November 2017
Remarks on composite Bernstein copula and its application to credit risk analysis
Publication date: November 2017
Source:Insurance: Mathematics and Economics, Volume 77 Author(s): Nan Guo, Fang Wang, Jingping Yang The composite Bernstein copula (CBC) (Yang et al., 2015) is a copula function generated from a composition of two copulas. This paper first shows that some well-known copulas belong to the CBC family with desirable properties. An EM algorithm for estimating the CBC is proposed, and it is applied for a real dataset to show the fitting result of the CBC in modeling dependence. The probabilistic structure for the CBC family is presented, which is useful for generating random numbers from the CBC. Finally, the probabilistic structure of the CBC is applied to credit risk analysis of collateralized debt obligations to show its advantage in empirical analysis.
November 2017
A general approach to full-range tail dependence copulas
Publication date: November 2017
Source:Insurance: Mathematics and Economics, Volume 77 Author(s): Jianxi Su, Lei Hua Full-range tail dependence copulas have recently been proved very useful for modeling various dependence patterns in the joint distributional tails. However, there are only a few applicable candidate models that have the full-range tail dependence property. In this paper, we present a general approach to constructing bivariate copulas that have full-range tail dependence in both upper and lower tails and are able to account for both reflection symmetry and reflection asymmetry. The general approach is based on mixtures of positive regularly varying random variables, and the full-range tail dependence property is established for such a general model. In order to construct copulas that possess the above dependence properties and are fast to compute, we construct a full-range tail dependence copula based on mixtures of Pareto random variables. We derive dependence properties of the proposed copula, and the extreme value copula based on it. A comparison with the full-range tail dependence copula proposed in Hua (2017) has been conducted, and the computational speed has been largely improved by the copula proposed in the current paper.
November 2017
Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions
Publication date: November 2017
Source:Insurance: Mathematics and Economics, Volume 77 Author(s): Tom Reynkens, Roel Verbelen, Jan Beirlant, Katrien Antonio In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modelling the whole range of the losses using a standard distribution is usually very hard and often impossible due to the specific characteristics of the body and the tail of the loss distribution. A possible solution is to combine two distributions in a splicing model: a light-tailed distribution for the body which covers light and moderate losses, and a heavy-tailed distribution for the tail to capture large losses. We propose a splicing model with a mixed Erlang (ME) distribution for the body and a Pareto distribution for the tail. This combines the flexibility of the ME distribution with the ability of the Pareto distribution to model extreme values. We extend our splicing approach for censored and/or truncated data. Relevant examples of such data can be found in financial risk analysis. We illustrate the flexibility of this splicing model using practical examples from risk measurement.
November 2017
Interplay of subexponential and dependent insurance and financial risks
Publication date: November 2017
Source:Insurance: Mathematics and Economics, Volume 77 Author(s): Yiqing Chen We are interested in the ruin probability of an insurer who makes risky investments and hence faces both insurance and financial risks. Assume that the insurance and financial risks over individual periods, $( X i , Y i )$,