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A life insurance model with asymmetric time preferences 具有非对称时间偏好的人寿保险模型
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-07-31 DOI: 10.1016/j.insmatheco.2024.07.005
Joakim Alderborn
{"title":"A life insurance model with asymmetric time preferences","authors":"Joakim Alderborn","doi":"10.1016/j.insmatheco.2024.07.005","DOIUrl":"10.1016/j.insmatheco.2024.07.005","url":null,"abstract":"<div><p>We build a life insurance model in the tradition of <span><span>Richard (1975)</span></span> and <span><span>Pliska and Ye (2007)</span></span>. Two agents purchase life insurance by continuously paying two premiums. At the random time of death of an agent, the life insurance payment is added to the household wealth to be used by the other agent. We allow for the agents to discount future utilities at different rates, which implies that the household has inconsistent time preferences. To solve the model, we employ the equilibrium of <span><span>Ekeland and Lazrak (2010)</span></span>, and we derive a new dynamic programming equation which is designed to find this equilibrium for our model. The most important contribution of the paper is to combine the issue of inconsistent time preferences with the presence of several agents. We also investigate the sensitivity of the behaviors of the agents to the parameters of the model by using numeric analysis. We find, among other things, that while the purchase of life insurance of one agent increases in her own discount rate, it decreases in the discount rate of the other agent.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"119 ","pages":"Pages 17-31"},"PeriodicalIF":1.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941732","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}
引用次数: 0
Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity 具有生物识别风险、习惯养成和平稳模糊性的最佳投资组合和保险策略
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-07-15 DOI: 10.1016/j.insmatheco.2024.07.002
Tao Wang , Zhiping Chen
{"title":"Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity","authors":"Tao Wang ,&nbsp;Zhiping Chen","doi":"10.1016/j.insmatheco.2024.07.002","DOIUrl":"10.1016/j.insmatheco.2024.07.002","url":null,"abstract":"<div><p>This paper studies the optimal consumption, investment, health insurance and life insurance strategy for a wage earner with smooth ambiguity, habit formation and biometric risks. The individual can invest in the financial market composed of a risk-free asset and a risky asset whose unknown market price results in ambiguity. The habit formation depends on historical consumption and satisfies an ordinary differential equation. Moreover, the biometric risks, which consist of health shock risk and mortality risk, can impact the individual's income and health state. The individual can purchase health insurance and life insurance to respectively deal with health shock risk and mortality risk, and aims at maximizing the total expected utility of consumption, legacy and terminal wealth. Using the dynamic programming technique, we derive the corresponding Hamilton-Jacobi-Bellman equation in the states of health and critical illness respectively, prove the verification theorem and obtain closed-form solutions for the optimal strategies. Finally, numerical experiments are carried out to illustrate the impact of risk aversion, ambiguity aversion, health shock and habit formation on the optimal strategy. The results reveal that the wage earner with different utility functions and different health states will show different behaviors in consumption, investment and insurance purchase.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 195-222"},"PeriodicalIF":1.9,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141704097","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}
引用次数: 0
Precautionary risk-reduction and saving decisions: Two sides of the same coin? 预防性降低风险和储蓄决策：一枚硬币的两面？
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-07-14 DOI: 10.1016/j.insmatheco.2024.07.001
Richard Peter , Annette Hofmann
{"title":"Precautionary risk-reduction and saving decisions: Two sides of the same coin?","authors":"Richard Peter ,&nbsp;Annette Hofmann","doi":"10.1016/j.insmatheco.2024.07.001","DOIUrl":"10.1016/j.insmatheco.2024.07.001","url":null,"abstract":"<div><p>We provide new results about the comparative static effects of income risk and interest rate risk on optimal risk-reduction and saving decisions. We combine arguments from the risk apportionment literature with monotone comparative statics. Risk reduction and saving are Edgeworth-Pareto substitutes for (mixed) risk averters and Edgeworth-Pareto complements for (mixed) risk lovers. For changes in income risk, risk reduction and saving are <em>N</em>th-degree risk complements for risk lovers. For changes in interest rate risk, risk reduction and saving are <em>N</em>th-degree risk substitutes for risk averters. The individual's risk attitude and the source of risk thus co-determine the effects of risk changes on optimal. We also discuss several extensions including multiple loss states, higher-order risk reduction, stochastic dominance, non-separable utility, and inflation risk.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 175-194"},"PeriodicalIF":1.9,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141636972","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}
引用次数: 0
A buy-hold-sell pension saving strategy 买入持有卖出的养老金储蓄策略
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-07-14 DOI: 10.1016/j.insmatheco.2024.07.003
Gaurav Khemka , Mogens Steffensen , Geoffrey J. Warren
{"title":"A buy-hold-sell pension saving strategy","authors":"Gaurav Khemka ,&nbsp;Mogens Steffensen ,&nbsp;Geoffrey J. Warren","doi":"10.1016/j.insmatheco.2024.07.003","DOIUrl":"10.1016/j.insmatheco.2024.07.003","url":null,"abstract":"<div><p>We propose a ‘buy, hold, sell’ (<em>BHS</em>) deterministic lifecycle strategy that involves buying and holding assets until they are sold to generate income. Savings are invested entirely into a risky portfolio until a pre-specified ‘switch age’ and then entirely into a risk-free portfolio after the switch age, followed by withdrawing during the payout phase from both portfolios based on annuitization factors that vary with age. We also allow for access to mortality credits through an insurance market. We analytically derive the dynamics of the investment strategy and show that the strategy is optimal for a range of investors with HARA risk preferences. We demonstrate numerically that the <em>BHS</em> strategy delivers limited loss of utility versus an optimal solution for investors with CRRA preferences and low-moderate levels of risk aversion while significantly outperforming deterministic strategies commonly seen in practice. The <em>BHS</em> strategy offers an attractive alternative for practical applications as it is straightforward to apply while avoiding the need for dynamic optimization and portfolio rebalancing.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"119 ","pages":"Pages 1-16"},"PeriodicalIF":1.9,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000799/pdfft?md5=5d3e103ca184df5987aeefd983a080cd&pid=1-s2.0-S0167668724000799-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141711413","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}
引用次数: 0
Convex and Lorenz orders under balance correction in nonlife insurance pricing: Review and new developments 非寿险定价平衡校正下的凸阶和洛伦兹阶：回顾与新发展
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-06-28 DOI: 10.1016/j.insmatheco.2024.06.003
Michel Denuit , Julien Trufin
{"title":"Convex and Lorenz orders under balance correction in nonlife insurance pricing: Review and new developments","authors":"Michel Denuit ,&nbsp;Julien Trufin","doi":"10.1016/j.insmatheco.2024.06.003","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.06.003","url":null,"abstract":"<div><p>By exploiting massive amounts of data, machine learning techniques provide actuaries with predictors exhibiting high correlation with claim frequencies and severities. However, these predictors generally fail to achieve financial equilibrium and thus do not qualify as pure premiums. Autocalibration effectively addresses this issue since it ensures that every group of policyholders paying the same premium is on average self-financing. Balance correction has been proposed as a way to make any candidate premium autocalibrated with the added advantage that it improves out-of-sample Bregman divergence and hence predictive Tweedie deviance. This paper proves that balance correction is also beneficial in terms of concentration curves and derives conditions ensuring that the initial predictor and its balance-corrected version are ordered in Lorenz order. Finally, criteria are proposed to rank the balance-corrected versions of two competing predictors in the convex order.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 123-128"},"PeriodicalIF":1.9,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141485064","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}
引用次数: 0
Correlation aversion and bivariate stochastic dominance with respect to reference functions 参考函数的相关厌恶和双变量随机优势
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-06-28 DOI: 10.1016/j.insmatheco.2024.06.005
Jingyuan Li , Jianli Wang , Lin Zhou
{"title":"Correlation aversion and bivariate stochastic dominance with respect to reference functions","authors":"Jingyuan Li ,&nbsp;Jianli Wang ,&nbsp;Lin Zhou","doi":"10.1016/j.insmatheco.2024.06.005","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.06.005","url":null,"abstract":"<div><p>This paper introduces an extension of stochastic dominance, moving from univariate to bivariate analysis by incorporating a reference function. Our approach offers flexibility in reference function selection, improving upon previous studies cohesively. Bivariate orderings are invaluable tools in actuarial sciences, facilitating the assessment and management of dependencies between risks and lifelengths within multiple insurance contracts. These advancements hold promising practical implications, particularly within the actuarial sciences domain.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 157-174"},"PeriodicalIF":1.9,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141594430","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}
引用次数: 0
Comparing and quantifying tail dependence 比较和量化尾部依赖性
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-06-26 DOI: 10.1016/j.insmatheco.2024.06.006
Karl Friedrich Siburg , Christopher Strothmann , Gregor Weiß
{"title":"Comparing and quantifying tail dependence","authors":"Karl Friedrich Siburg ,&nbsp;Christopher Strothmann ,&nbsp;Gregor Weiß","doi":"10.1016/j.insmatheco.2024.06.006","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.06.006","url":null,"abstract":"<div><p>We introduce a new stochastic order for the tail dependence between random variables. We then study different measures of tail dependence which are monotone in the proposed order, thereby extending various known tail dependence coefficients from the literature. We apply our concepts in an empirical study where we investigate the tail dependence for different pairs of S&amp;P 500 stocks and indices, and illustrate the advantage of our measures of tail dependence over the classical tail dependence coefficient.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 95-103"},"PeriodicalIF":1.9,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000775/pdfft?md5=439d0fecf61841697a63f37fba351140&pid=1-s2.0-S0167668724000775-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141485062","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}
引用次数: 0
Probabilistic approach to risk processes with level-dependent premium rate 用概率方法处理保费率取决于水平的风险过程
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-06-26 DOI: 10.1016/j.insmatheco.2024.06.002
Denis Denisov , Niklas Gotthardt , Dmitry Korshunov , Vitali Wachtel
{"title":"Probabilistic approach to risk processes with level-dependent premium rate","authors":"Denis Denisov ,&nbsp;Niklas Gotthardt ,&nbsp;Dmitry Korshunov ,&nbsp;Vitali Wachtel","doi":"10.1016/j.insmatheco.2024.06.002","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.06.002","url":null,"abstract":"<div><p>We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift.</p><p>We show that such risk processes give rise to heavy-tailed ruin probabilities whatever the distribution of the claim size, even if it is a bounded random variable. So, the risk processes with near critical premium rate provide an important example of a stochastic model where light-tailed input produces heavy-tailed output.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 142-156"},"PeriodicalIF":1.9,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167668724000726/pdfft?md5=6232f72c323d396a7391ed63b243cb59&pid=1-s2.0-S0167668724000726-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141594429","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}
引用次数: 0
Stochastic orders and distortion risk contribution ratio measures 随机阶次和扭曲风险贡献率测量法
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-06-25 DOI: 10.1016/j.insmatheco.2024.06.007
Yiying Zhang
{"title":"Stochastic orders and distortion risk contribution ratio measures","authors":"Yiying Zhang","doi":"10.1016/j.insmatheco.2024.06.007","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.06.007","url":null,"abstract":"<div><p>Relative spillover effects play a crucial role in the analysis and comparison of systemic risks. This paper introduces a novel approach, referred to as distortion risk contribution ratio measures, for quantifying such effects. Various types of contribution ratio measures are defined based on the newly proposed conditional distortion risk measures by <span>Dhaene et al. (2022)</span>, and useful integral-based representations are provided as well. An interesting equivalent characterization result for the convex transform order is also presented, which is not only relevant to proving our main results but also has independent value in other research areas. We then establish comparison results between the distortion risk contribution ratio measures of two different bivariate random vectors with either the same or different copulas. Sufficient conditions are established in terms of stochastic orders, copula functions, distortion functions, and stress levels. Furthermore, we investigate the ordering behaviors of these measures in relation to the interaction between paired risks. Numerical examples are presented to illustrate the conditions and main findings.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 104-122"},"PeriodicalIF":1.9,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141485063","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}
引用次数: 0
Are reference measures of law-invariant functionals unique? 定律不变函数的参考测量值是唯一的吗？
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-06-21 DOI: 10.1016/j.insmatheco.2024.06.004
Felix-Benedikt Liebrich
{"title":"Are reference measures of law-invariant functionals unique?","authors":"Felix-Benedikt Liebrich","doi":"10.1016/j.insmatheco.2024.06.004","DOIUrl":"https://doi.org/10.1016/j.insmatheco.2024.06.004","url":null,"abstract":"<div><p>A functional defined on random variables <em>f</em> is law invariant with respect to a reference probability if its value only depends on the distribution of its argument <em>f</em> under that measure. In contrast to most of the literature on the topic, we take a concrete functional as given and ask if there can be more than one such reference probability. For wide classes of functionals – including, for instance, monetary risk measures and return risk measures – we demonstrate that this is not the case <em>unless</em> they are (i) constant, or (ii) more generally depend only on the essential infimum and essential supremum of the argument <em>f</em>. Mathematically, the results leverage Lyapunov's Convexity Theorem.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 129-141"},"PeriodicalIF":1.9,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016766872400074X/pdfft?md5=ce86509697eaf6efc4ed47083246b5f6&pid=1-s2.0-S016766872400074X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141540202","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}
引用次数: 0
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