Insurance Mathematics & Economics最新文献

{"title":"A new class of composite GBII regression models with varying threshold for modeling heavy-tailed data","authors":"Zhengxiao Li ,&nbsp;Fei Wang ,&nbsp;Zhengtang Zhao","doi":"10.1016/j.insmatheco.2024.03.005","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.03.005","url":null,"abstract":"<div><p>The four-parameter generalized beta distribution of the second kind (GBII) has been proposed for modeling insurance losses with heavy-tailed features. The aim of this paper is to present a parametric composite GBII regression modeling by splicing two GBII distributions using mode matching method. It is designed for simultaneous modeling of small and large claims and capturing the policyholder heterogeneity by introducing the covariates into the scale parameter. The threshold that splits two GBII distributions is allowed to vary across individuals policyholders based on their risk features. The proposed regression modeling also contains a wide range of insurance loss distributions as the head and the tail respectively and provides the close-formed expressions for parameter estimation and model prediction. A simulation study is conducted to show the accuracy of the proposed estimation method and the flexibility of the regressions. Some illustrations of the applicability of the new class of distributions and regressions are provided with a Danish fire losses data set and a Chinese medical insurance claims data set, comparing with the results of competing models from the literature.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"117 ","pages":"Pages 45-66"},"PeriodicalIF":1.9,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140638783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust asset-liability management games for n players under multivariate stochastic covariance models","authors":"Ning Wang ,&nbsp;Yumo Zhang","doi":"10.1016/j.insmatheco.2024.04.001","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.04.001","url":null,"abstract":"<div><p>This paper investigates a non-zero-sum stochastic differential game among <em>n</em> competitive CARA asset-liability managers, who are concerned about the potential model ambiguity and aim to seek the robust investment strategies. The ambiguity-averse managers are subject to uncontrollable and idiosyncratic random liabilities driven by generalized drifted Brownian motions and have access to an incomplete financial market consisting of a risk-free asset, a market index and a stock under a multivariate stochastic covariance model. The market dynamics permit not only stochastic correlation between the risky assets but also path-dependent and time-varying risk premium and volatility, depending on two affine-diffusion factor processes. The objective of each manager is to maximize the expected exponential utility of his terminal surplus relative to the average among his competitors under the worst-case scenario of the alternative measures. We manage to solve this robust non-Markovian stochastic differential game by using a backward stochastic differential equation approach. Explicit expressions for the robust Nash equilibrium investment policies, the density generator processes under the well-defined worst-case probability measures and the corresponding value functions are derived. Conditions for the admissibility of the robust equilibrium strategies are provided. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium investment strategies and draw some economic interpretations from these results.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"117 ","pages":"Pages 67-98"},"PeriodicalIF":1.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140638468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal investment-disinvestment choices in health-dependent variable annuity","authors":"Guglielmo D'Amico ,&nbsp;Shakti Singh ,&nbsp;Dharmaraja Selvamuthu","doi":"10.1016/j.insmatheco.2024.03.006","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.03.006","url":null,"abstract":"<div><p>This paper exploits the influence of the policyholder's health status on the optimal time at which the policyholder decides to stop paying health-dependent premiums and starts withdrawing health-dependent benefits from a variable annuity (VA) contract accompanied by a guaranteed lifelong withdrawal benefit (GLWB). A mixed continuous-discrete time model is developed to find the optimal time for withdrawal regime initiation. The model determines the investment and disinvestment triggers according to the market conditions for both dynamic and static cases. In the static case, the optimal time is computed at the policy's inception time. In contrast, in the dynamic case, the optimal initiation time is achieved by recursive calculation of the exercise frontier of a real deferral option. Another finding is the sensitivity analysis of the contract concerning the insurance fee and the age of the policyholder.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"117 ","pages":"Pages 1-15"},"PeriodicalIF":1.9,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000416/pdfft?md5=bf726ab505fe9dd0f743a0c7baa16ca1&pid=1-s2.0-S0167668724000416-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140550785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal control under uncertainty: Application to the issue of CAT bonds","authors":"Nicolas Baradel","doi":"10.1016/j.insmatheco.2024.03.004","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.03.004","url":null,"abstract":"<div><p>We propose a general framework for studying optimal issue of CAT bonds in the presence of uncertainty on the parameters. In particular, the intensity of arrival of natural disasters is inhomogeneous and may depend on unknown parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayes rule. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. We provide examples of application in the context of hurricanes in Florida.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"117 ","pages":"Pages 16-44"},"PeriodicalIF":1.9,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140558584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Worst-case risk with unspecified risk preferences","authors":"Haiyan Liu","doi":"10.1016/j.insmatheco.2024.03.003","DOIUrl":"10.1016/j.insmatheco.2024.03.003","url":null,"abstract":"<div><p>In this paper, we study the worst-case distortion risk measure for a given risk when information about distortion functions is partially available. We obtain the explicit forms of the worst-case distortion functions for several different sets of plausible distortion functions. When there is no concavity constraint on distortion functions, the worst-case distortion function is independent of the risk to be measured and the corresponding worst-case distortion risk measure is the weighted average of the VaR's of the risk for all decision makers. When the concavity constraint is imposed on distortion functions and the set of concave distortion functions is defined by the riskiness of one single risk, the explicit form of the worst-case distortion function is obtained, which depends the risk to be measured. When the set of concave distortion functions is defined by the riskiness of multiple risks, we reduce the infinite-dimensional optimization problem to a finite-dimensional optimization problem which can be solved numerically. Finally, we apply the worst-case risk measure to optimal decision making in reinsurance.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 235-248"},"PeriodicalIF":1.9,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140268203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mean field game approach to optimal investment and risk control for competitive insurers","authors":"Lijun Bo ,&nbsp;Shihua Wang ,&nbsp;Chao Zhou","doi":"10.1016/j.insmatheco.2024.03.002","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.03.002","url":null,"abstract":"<div><p>We consider an insurance market consisting of multiple competitive insurers with a mean field interaction via their terminal wealth under the exponential utility with relative performance. It is assumed that each insurer regulates her risk by controlling the number of policies. We respectively establish the constant Nash equilibrium (independent of time) on the investment and risk control strategy for the finite <em>n</em>-insurer game and the constant mean field equilibrium for the corresponding mean field game (MFG) problem (when the number of insurers tends to infinity). Furthermore, we examine the convergence relationship between the constant Nash equilibrium of finite <em>n</em>-insurer game and the mean field equilibrium of the corresponding MFG problem. Our numerical analysis reveals that, for a highly competitive insurance market consisting of many insurers, every insurer will invest more in risky assets and increase the total number of outstanding liabilities to maximize her exponential utility with relative performance.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 202-217"},"PeriodicalIF":1.9,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140163355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tail mean-variance portfolio selection with estimation risk","authors":"Zhenzhen Huang ,&nbsp;Pengyu Wei ,&nbsp;Chengguo Weng","doi":"10.1016/j.insmatheco.2024.03.001","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.03.001","url":null,"abstract":"<div><p>Tail Mean-Variance (TMV) has emerged from the actuarial community as a criterion for risk management and portfolio selection, with a focus on extreme losses. The existing literature on portfolio optimization under the TMV criterion relies on the plug-in approach that substitutes the unknown mean vector and covariance matrix of asset returns in the optimal portfolio weights with their sample counterparts. However, the plug-in method inevitably introduces estimation risk and usually leads to poor out-of-sample portfolio performance. To address this issue, we propose a combination of the plug-in and 1/N rules and optimize its expected out-of-sample performance. Our study is based on the Mean-Variance-Standard-deviation (MVS) performance measure, which encompasses the TMV, classical Mean-Variance, and Mean-Standard-Deviation (MStD) as special cases. The MStD criterion is particularly relevant to mean-risk portfolio selection when risk is measured by quantile-based risk measures. Our proposed combined portfolio consistently outperforms both the plug-in MVS and 1/N portfolios in simulated and real-world datasets.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 218-234"},"PeriodicalIF":1.9,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140180811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stackelberg equilibria with multiple policyholders","authors":"Mario Ghossoub,&nbsp;Michael B. Zhu","doi":"10.1016/j.insmatheco.2024.02.008","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.02.008","url":null,"abstract":"<div><p>We examine Pareto-efficient contracts and Stackelberg Equilibria (SE) in a sequential-move insurance market in which a central monopolistic insurer on the supply side contracts with multiple policyholders on the demand side. We obtain a representation of Pareto-efficient contracts when the monopolistic insurer's preferences are represented by a coherent risk measure. We then obtain a representation of SE in this market, and we show that the contracts induced by an SE are Pareto-efficient. However, we note that SE do not induce a welfare gain to the policyholders in this case, echoing the conclusions of recent work in the literature. The social welfare implications of this finding are examined through an application to the flood insurance market of the United States of America, in which we find that the central insurer has a strong incentive to raise premia to the detriment of the policyholders. Accordingly, we argue that monopolistic insurance markets are problematic, and must be appropriately addressed by external regulation.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 189-201"},"PeriodicalIF":1.9,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140123172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Risk quantization by magnitude and propensity","authors":"Olivier P. Faugeras ,&nbsp;Gilles Pagès","doi":"10.1016/j.insmatheco.2024.02.005","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.02.005","url":null,"abstract":"<div><p>We propose a novel approach in the assessment of a random risk variable <em>X</em> by introducing magnitude-propensity risk measures <span><math><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span>. This bivariate measure intends to account for the dual aspect of risk, where the magnitudes <em>x</em> of <em>X</em> tell how high are the losses incurred, whereas the probabilities <span><math><mi>P</mi><mo>(</mo><mi>X</mi><mo>=</mo><mi>x</mi><mo>)</mo></math></span> reveal how often one has to expect to suffer such losses. The basic idea is to simultaneously quantify both the severity <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> and the propensity <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> of the real-valued risk <em>X</em>. This is to be contrasted with traditional univariate risk measures, like VaR or CVaR, which typically conflate both effects. In its simplest form, <span><math><mo>(</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span> is obtained by mass transportation in Wasserstein metric of the law of <em>X</em> to a two-points <span><math><mo>{</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>}</mo></math></span> discrete distribution with mass <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> at <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>. The approach can also be formulated as a constrained optimal quantization problem. This allows for an informative comparison of risks on both the magnitude and propensity scales. Several examples illustrate the usefulness of the proposed approach. Some variants, extensions and applications are also considered.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 134-147"},"PeriodicalIF":1.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000325/pdfft?md5=980ec9ef940c4445bf5515f1cd52e4b3&pid=1-s2.0-S0167668724000325-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140041443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pooling functional disability and mortality in long-term care insurance and care annuities: A matrix approach for multi-state pools","authors":"Doreen Kabuche,&nbsp;Michael Sherris,&nbsp;Andrés M. Villegas,&nbsp;Jonathan Ziveyi","doi":"10.1016/j.insmatheco.2024.02.006","DOIUrl":"10.1016/j.insmatheco.2024.02.006","url":null,"abstract":"<div><p>Mortality risk sharing pools including group self-annuitisation, pooled annuity funds and tontines have been developed as an effective solution for managing longevity risk. Although they have been widely studied in the literature, these mortality risk sharing pools do not consider individual health or functional disability status nor the need for long-term care (LTC) insurance at older ages. We extend these pools to include functional disability and chronic illness and present a matrix-based methodology for pooling mortality risk across heterogeneous individuals classified by functional disability states and chronic illness statuses. We demonstrate how individuals with different health risks can more equitably share mortality risk in a pooled annuity design. A multi-state pool is formed by pooling annuitants considering both longevity and LTC risks and determining the actuarially fair benefits based on individuals' health states. Our methodology provides a general structure for a pooled annuity product that can be applied for general multi-state models. We present an extensive analysis with numerical examples using the US Health and Retirement Study (HRS) data. Our results compare expected annuity benefits for individuals in poor health to those in good health, show the effects of incorporating systematic trends and uncertainty, assess how the valuation of the expected annuity payments interacts with the assumptions used for the multi-state model and assess the impact of pool size.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"116 ","pages":"Pages 165-188"},"PeriodicalIF":1.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000349/pdfft?md5=5a4f32034b212febb88f047db5c12dad&pid=1-s2.0-S0167668724000349-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140089699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}