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.
{"title":"Optimal investment-disinvestment choices in health-dependent variable annuity","authors":"Guglielmo D'Amico , Shakti Singh , 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":null,"pages":null},"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}
Pub Date : 2024-03-28DOI: 10.1016/j.insmatheco.2024.03.004
Nicolas Baradel
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.
{"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":null,"pages":null},"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}
Pub Date : 2024-03-19DOI: 10.1016/j.insmatheco.2024.03.003
Haiyan Liu
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.
{"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":null,"pages":null},"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}
Pub Date : 2024-03-15DOI: 10.1016/j.insmatheco.2024.03.002
Lijun Bo , Shihua Wang , Chao Zhou
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 n-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 n-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.
我们考虑的是一个由多家竞争性保险公司组成的保险市场,在指数效用和相对业绩的作用下,这些保险公司通过其终端财富进行均值场互动。假设每个保险公司都通过控制保单数量来调节风险。我们分别建立了有限 n 保险人博弈中投资和风险控制策略的恒定纳什均衡(与时间无关),以及相应均值场博弈(MFG)问题的恒定均值场均衡(当保险人数量趋于无穷大时)。此外,我们还研究了有限 n 保险人博弈的恒定纳什均衡与相应 MFG 问题的均值场均衡之间的收敛关系。我们的数值分析表明,对于一个由众多保险公司组成的竞争激烈的保险市场,每个保险公司都会更多地投资于风险资产,并增加未偿付负债的总数,以最大化其指数效用的相对表现。
{"title":"A mean field game approach to optimal investment and risk control for competitive insurers","authors":"Lijun Bo , Shihua Wang , 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":null,"pages":null},"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}
Pub Date : 2024-03-12DOI: 10.1016/j.insmatheco.2024.03.001
Zhenzhen Huang , Pengyu Wei , Chengguo Weng
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.
{"title":"Tail mean-variance portfolio selection with estimation risk","authors":"Zhenzhen Huang , Pengyu Wei , 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":null,"pages":null},"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}
Pub Date : 2024-03-08DOI: 10.1016/j.insmatheco.2024.02.008
Mario Ghossoub, Michael B. Zhu
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.
我们研究了一个连续移动的保险市场中的帕累托效率合同和斯塔克尔伯格均衡(SE),在这个市场中,供应方的中央垄断保险人与需求方的多个投保人签订合同。当垄断保险人的偏好由一致的风险度量来表示时,我们得到了帕累托效率合同的表示。然后,我们得到了 SE 在该市场中的表现形式,并证明由 SE 诱导的合同是帕累托效率的。然而,我们注意到,在这种情况下,SE 不会给投保人带来福利收益,这与近期文献的结论不谋而合。我们将这一结论应用于美国的洪水保险市场,研究其对社会福利的影响,发现中央保险人有强烈的动机提高保险费率,从而损害投保人的利益。因此,我们认为垄断性保险市场是有问题的,必须通过外部监管加以适当解决。
{"title":"Stackelberg equilibria with multiple policyholders","authors":"Mario Ghossoub, 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":null,"pages":null},"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}
Pub Date : 2024-03-05DOI: 10.1016/j.insmatheco.2024.02.005
Olivier P. Faugeras , Gilles Pagès
We propose a novel approach in the assessment of a random risk variable X by introducing magnitude-propensity risk measures . This bivariate measure intends to account for the dual aspect of risk, where the magnitudes x of X tell how high are the losses incurred, whereas the probabilities reveal how often one has to expect to suffer such losses. The basic idea is to simultaneously quantify both the severity and the propensity of the real-valued risk X. This is to be contrasted with traditional univariate risk measures, like VaR or CVaR, which typically conflate both effects. In its simplest form, is obtained by mass transportation in Wasserstein metric of the law of X to a two-points discrete distribution with mass at . 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.
我们提出了一种评估随机风险变量 X 的新方法,即引入风险概率(mX,pX)。这种二元风险度量旨在考虑风险的双重性,即 X 的大小 x 反映了所造成的损失有多大,而概率 P(X=x) 则揭示了人们预期遭受此类损失的频率有多高。其基本思想是同时量化实值风险 X 的严重性 mX 和倾向性 pX,这与传统的单变量风险度量(如 VaR 或 CVaR)不同,后者通常将两种效应混为一谈。在最简单的形式中,(mX,pX) 是通过将 X 的规律以 Wasserstein 度量进行质量运算得到的,即在 mX 处具有质量 pX 的两点{0,mX}离散分布。该方法也可表述为受约束的最优量化问题。这样就可以对风险大小和倾向尺度进行信息比较。几个例子说明了所提方法的实用性。此外,还考虑了一些变体、扩展和应用。
{"title":"Risk quantization by magnitude and propensity","authors":"Olivier P. Faugeras , 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":null,"pages":null},"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}
Pub Date : 2024-03-01DOI: 10.1016/j.insmatheco.2024.02.006
Doreen Kabuche, Michael Sherris, Andrés M. Villegas, Jonathan Ziveyi
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.
{"title":"Pooling functional disability and mortality in long-term care insurance and care annuities: A matrix approach for multi-state pools","authors":"Doreen Kabuche, Michael Sherris, Andrés M. Villegas, 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":null,"pages":null},"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}
Quantiles of the mortality rates are relevant in life insurance to control longevity risk properly. Recently, Santolino (2020) adapts the framework of the popular Lee-Carter model to compute the conditional quantiles of the mortality rates. The parameters of the quantile Lee-Carter model are fitted on the mortality data of the population of interest, ignoring the information related to the others. In this paper, we show that more robust parameter estimates can be obtained exploiting the mortality experiences of multiple populations. A neural network is employed to calibrate individual quantile Lee-Carter models jointly using all the available mortality data. In this setting, some common network parameters are used to learn the age and period effects of multiple quantile LC models. Numerical experiments performed on all the countries of the Human Mortality Database validate our approach. The predictions obtained considering the median level appear more accurate than those obtained with the mean models; moreover, those at the tail quantile levels capture the future mortality evolution of the populations well.
{"title":"Quantile mortality modelling of multiple populations via neural networks","authors":"Stefania Corsaro, Zelda Marino, Salvatore Scognamiglio","doi":"10.1016/j.insmatheco.2024.02.007","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.02.007","url":null,"abstract":"<div><p>Quantiles of the mortality rates are relevant in life insurance to control longevity risk properly. Recently, <span>Santolino (2020)</span> adapts the framework of the popular Lee-Carter model to compute the conditional quantiles of the mortality rates. The parameters of the quantile Lee-Carter model are fitted on the mortality data of the population of interest, ignoring the information related to the others. In this paper, we show that more robust parameter estimates can be obtained exploiting the mortality experiences of multiple populations. A neural network is employed to calibrate individual quantile Lee-Carter models jointly using all the available mortality data. In this setting, some common network parameters are used to learn the age and period effects of multiple quantile LC models. Numerical experiments performed on all the countries of the Human Mortality Database validate our approach. The predictions obtained considering the median level appear more accurate than those obtained with the mean models; moreover, those at the tail quantile levels capture the future mortality evolution of the populations well.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140041442","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}
Pub Date : 2024-02-24DOI: 10.1016/j.insmatheco.2024.02.004
Francesco Ungolo , Edwin R. van den Heuvel
We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is flexibly characterized by a random effect which follows a discrete probability distribution drawn from a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance portfolio previously analysed by Milhaud and Dutang (2018). The approach yields an improved predictive performance of the surrending rates.
{"title":"A Dirichlet process mixture regression model for the analysis of competing risk events","authors":"Francesco Ungolo , Edwin R. van den Heuvel","doi":"10.1016/j.insmatheco.2024.02.004","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.02.004","url":null,"abstract":"<div><p>We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is flexibly characterized by a random effect which follows a discrete probability distribution drawn from a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance portfolio previously analysed by <span>Milhaud and Dutang (2018)</span>. The approach yields an improved predictive performance of the surrending rates.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000295/pdfft?md5=9e941f043f3f798aedb74fba46ba6dc0&pid=1-s2.0-S0167668724000295-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139993140","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}