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A new characterization of second-order stochastic dominance 二阶随机优势的新特征
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-10-11 DOI: 10.1016/j.insmatheco.2024.09.005
{"title":"A new characterization of second-order stochastic dominance","authors":"","doi":"10.1016/j.insmatheco.2024.09.005","DOIUrl":"10.1016/j.insmatheco.2024.09.005","url":null,"abstract":"<div><div>We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the resulting position generally less desirable for risk-averse agents. A similar characterization is also found for convex order and increasing convex order. The proof techniques for the main result are based on properties of Expected Shortfall, a family of risk measures that is popular in banking and insurance regulation. Applications in risk management and insurance are discussed.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433953","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
Bivariate Tail Conditional Co-Expectation for elliptical distributions 椭圆分布的双变量尾部条件共期望
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-10-01 DOI: 10.1016/j.insmatheco.2024.09.004
{"title":"Bivariate Tail Conditional Co-Expectation for elliptical distributions","authors":"","doi":"10.1016/j.insmatheco.2024.09.004","DOIUrl":"10.1016/j.insmatheco.2024.09.004","url":null,"abstract":"<div><div>In this paper, we consider a random vector <span><math><mi>X</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></math></span> following a multivariate Elliptical distribution and we provide an explicit formula for <span><math><mi>E</mi><mrow><mo>(</mo><mi>X</mi><mo>|</mo><mi>X</mi><mo>≤</mo><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></mrow></math></span>, i.e., the expected value of the bivariate random variable <em>X</em> conditioned to the event <span><math><mi>X</mi><mo>≤</mo><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span>, with <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. Such a conditional expectation has an intuitive interpretation in the context of risk measures. Specifically, <span><math><mi>E</mi><mrow><mo>(</mo><mi>X</mi><mo>|</mo><mi>X</mi><mo>≤</mo><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></mrow></math></span> can be interpreted as the Tail Conditional Co-Expectation of <em>X</em> (TCoES). Our main result analytically proves that for a large number of Elliptical distributions, the TCoES can be written as a function of the probability density function of the Skew Elliptical distributions introduced in the literature by the pioneering work of <span><span>Azzalini (1985)</span></span>. Some numerical experiments based on empirical data show the usefulness of the obtained results for real-world applications.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419356","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
Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat? 平均分摊和分担长寿风险，又称 "管理人能否帮助猫剥皮"？
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-09-30 DOI: 10.1016/j.insmatheco.2024.09.003
{"title":"Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?","authors":"","doi":"10.1016/j.insmatheco.2024.09.003","DOIUrl":"10.1016/j.insmatheco.2024.09.003","url":null,"abstract":"<div><div>This paper is concerned with the mathematical problem of allocating longevity-linked fund payouts in a pool where participants differ in both wealth (contributions) and health (mortality), particularly when these groups are relatively small in size. In other words, we offer a modelling framework for distributing longevity-risk pools' income and benefits (or “tontine winnings”) when participants are heterogeneous. Similar to the nascent literature on decentralized risk sharing (DRS), there are several equally plausible arrangements for sharing benefits (a.k.a. “skinning the tontine cat”) among survivors. We argue that the selected rule may depend on the extent of social cohesion within the longevity risk pool, ranging from solidarity and altruism to pure individualism. And, if actuarial fairness is a concern, we suggest introducing an administrator – which differs from a guarantor – to make the tontine pool payouts collectively actuarial fair. Fairness is in the sense that the group of participants will on average receive the same benefits as they collectively invested; and we provide the mathematical framework to implement that suggestion. One thing is for certain: actuarial science cannot offer design uniqueness for longevity-contingent claims; only a consistent methodology.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419355","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 two-layer stochastic game approach to reinsurance contracting and competition 再保险合约和竞争的双层随机博弈方法
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-09-27 DOI: 10.1016/j.insmatheco.2024.09.002
{"title":"A two-layer stochastic game approach to reinsurance contracting and competition","authors":"","doi":"10.1016/j.insmatheco.2024.09.002","DOIUrl":"10.1016/j.insmatheco.2024.09.002","url":null,"abstract":"<div><div>We propose a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle. The reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus, and their competition is settled by a noncooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semiclosed form. Furthermore, we obtain interesting sensitivity results for the equilibrium strategies through both analytical and numerical studies.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356783","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 insurance design under asymmetric Nash bargaining 非对称纳什谈判下的最优保险设计
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-09-12 DOI: 10.1016/j.insmatheco.2024.08.006
{"title":"Optimal insurance design under asymmetric Nash bargaining","authors":"","doi":"10.1016/j.insmatheco.2024.08.006","DOIUrl":"10.1016/j.insmatheco.2024.08.006","url":null,"abstract":"<div><p>This paper considers a risk-neutral insurer and a risk-averse individual who bargain over the terms of an insurance contract. Under asymmetric Nash bargaining, we show that the Pareto-optimal insurance contract always contains a straight deductible under linear transaction costs and that the deductible disappears if and only if the deadweight cost is zero, regardless of the insurer's bargaining power. We further find that the optimality of no insurance is consistent across all market structures. When the insured's risk preference exhibits decreasing absolute risk aversion, the optimal deductible and the insurer's expected loss decrease in the degree of the insured's risk aversion and thus increase in the insured's initial wealth. In addition, the effect of increasing the insurer's bargaining power on the optimal deductible is equivalent to a pure effect of reducing the initial wealth of the insured. Our results suggest that the well-documented preference for low deductibles could be the result of insurance bargaining.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142233639","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
Valuation of guaranteed lifelong withdrawal benefit with the long-term care option 采用长期护理方案的有保障终身离职金估值
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-09-07 DOI: 10.1016/j.insmatheco.2024.09.001
{"title":"Valuation of guaranteed lifelong withdrawal benefit with the long-term care option","authors":"","doi":"10.1016/j.insmatheco.2024.09.001","DOIUrl":"10.1016/j.insmatheco.2024.09.001","url":null,"abstract":"<div><p>In this paper, under the stochastic interest rate framework, we consider the valuation of a Guaranteed Lifelong Withdrawal Benefit (GLWB) annuity product by explicitly incorporating the health state of the policyholder through the long-term care (LTC) option. The product provides policyholders with protection against longevity risk and market downturns, as well as financial support when facing LTC needs. Within the context of dynamic withdrawals, the valuation of the GLWB annuity with the LTC option is characterized as a stochastic optimal control problem. We introduce a novel bang-bang analysis approach without the usual convexity assumption in literature and prove that the optimal withdrawal strategies for the policyholder are constrained to a finite set. Furthermore, we perform a sensitivity analysis on the price determinants of GLWB annuities with and without the LTC option, and provide economic interpretations. Lastly, we investigate the impact of gender on the optimal withdrawal strategy and the fair fee of the annuity with the LTC option.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168313","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 dividends and capital injection: A general Lévy model with extensions to regime-switching models 最优股息和注资：扩展到制度转换模型的一般莱维模型
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-09-06 DOI: 10.1016/j.insmatheco.2024.08.007
{"title":"Optimal dividends and capital injection: A general Lévy model with extensions to regime-switching models","authors":"","doi":"10.1016/j.insmatheco.2024.08.007","DOIUrl":"10.1016/j.insmatheco.2024.08.007","url":null,"abstract":"<div><p>This paper studies a general Lévy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in the single-regime setting with a concave terminal payoff function. This is then applied to show the optimality of a Markov-modulated double barrier strategy in the regime-switching model via contraction mapping arguments. We solve these for a general Lévy model with both positive and negative jumps, greatly generalizing the existing results on spectrally one-sided models.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142241354","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 unified theory of decentralized insurance 分散式保险的统一理论
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-09-05 DOI: 10.1016/j.insmatheco.2024.08.008
{"title":"A unified theory of decentralized insurance","authors":"","doi":"10.1016/j.insmatheco.2024.08.008","DOIUrl":"10.1016/j.insmatheco.2024.08.008","url":null,"abstract":"<div><p>Decentralized insurance can be used to describe risk sharing mechanisms under which participants trade risks among each other as opposed to passing risks mostly to an insurer in traditional centralized insurance. There are a wide range of decentralized practices in all kinds of forms developed around the world, including online mutual aid in East Asia, takaful in the Middle East, peer-to-peer insurance in the West, international catastrophe risk pooling by African, Caribbean and Central America countries, etc. There is also a rich literature of risk sharing in academia that offers theoretical bases of other decentralized mechanisms. This work presents a unified mathematical framework to describe the commonalities and the relationships of all these seemingly different business in practice and theoretical models in academia. Such a framework provides a fertile ground for the comparison of existing practices and the design and engineering of hybrid and innovative models.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142164507","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
Uniqueness of equilibrium with survival probability heterogeneity and endogenous annuity price 具有生存概率异质性和内生年金价格的均衡唯一性
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-08-30 DOI: 10.1016/j.insmatheco.2024.08.004
{"title":"Uniqueness of equilibrium with survival probability heterogeneity and endogenous annuity price","authors":"","doi":"10.1016/j.insmatheco.2024.08.004","DOIUrl":"10.1016/j.insmatheco.2024.08.004","url":null,"abstract":"<div><p>When annuitants' survival probabilities are heterogeneous, the equilibrium annuity price is affected by their annuitization choices, which further depend on the annuity price. Given this mutual dependence, it is generally difficult to establish uniqueness of the equilibrium. Based on similar expressions appearing in several annuity and insurance models, we obtain two results in an annuity model with heterogeneity in survival probability only. First, the equilibrium annuity price is always unique if the annuitization function is multiplicatively separable in survival probability and annuity price. Second, the equilibrium is unique for more general annuitization functions, provided that a sufficient condition on the distribution of survival probabilities holds. Many distributions, including the uniform, normal and gamma distributions, satisfy this condition.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136699","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
Spatial copula-based modeling of claim frequency and claim size in third-party car insurance: A Poisson-mixed approach for predictive analysis 基于空间 copula 的第三方汽车保险索赔频率和索赔规模建模：用于预测分析的泊松混合方法
IF 1.9 2区 经济学
Insurance Mathematics & Economics Pub Date : 2024-08-26 DOI: 10.1016/j.insmatheco.2024.08.005
{"title":"Spatial copula-based modeling of claim frequency and claim size in third-party car insurance: A Poisson-mixed approach for predictive analysis","authors":"","doi":"10.1016/j.insmatheco.2024.08.005","DOIUrl":"10.1016/j.insmatheco.2024.08.005","url":null,"abstract":"<div><p>The number and amount of claims, referred to as the sum of claims or the total claim/loss amounts in insurance literature, are crucial pieces of information for insurance companies. The analysis of these numerical values can provide essential insights for targeted planning. This study explores a spatial approach for jointly modeling claim frequency and claim size. We assume that the number of accidents follows a Poisson distribution with a variable mean, and this mean, in turn, has a distribution commonly known as a mixed distribution. The spatial dependence structure within the observations is then modeled using an appropriate copula. By estimating the parameters of the proposed model, we draw prediction maps for both claim frequencies and total claim size. These maps will contribute to the prediction of future claim dynamics, offering insurers the opportunity to refine their market strategies and enhance their overall risk management approach based on evolving spatial patterns.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142087171","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
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