Insurance Mathematics & Economics最新文献

A risk measurement approach from risk-averse stochastic optimization of score functions 从分值函数的风险规避随机优化出发的风险测量方法

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2024-11-15 DOI: 10.1016/j.insmatheco.2024.11.005

Marcelo Brutti Righi, Fernanda Maria Müller, Marlon Ruoso Moresco

引用次数: 0

Comonotonicity and Pareto optimality, with application to collaborative insurance 协调性和帕累托最优性，适用于合作保险

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2024-11-12 DOI: 10.1016/j.insmatheco.2024.11.001

Michel Denuit , Jan Dhaene , Mario Ghossoub , Christian Y. Robert

{"title":"Comonotonicity and Pareto optimality, with application to collaborative insurance","authors":"Michel Denuit , Jan Dhaene , Mario Ghossoub , Christian Y. Robert","doi":"10.1016/j.insmatheco.2024.11.001","DOIUrl":"10.1016/j.insmatheco.2024.11.001","url":null,"abstract":"<div><div>Two by-now folkloric results in the theory of risk sharing are that (i) any feasible allocation is convex-order-dominated by a comonotonic allocation; and (ii) an allocation is Pareto optimal for the convex order if and only if it is comonotonic. Here, comonotonicity corresponds to the so-called <em>no-sabotage condition</em>, which aligns the interests of all parties involved. Several proofs of these two results have been provided in the literature, all based on a version of the comonotonic improvement algorithm of <span><span>Landsberger and Meilijson (1994)</span></span> and a limit argument based on the Martingale Convergence Theorem. However, no proof of (i) is explicit enough to allow for an easy algorithmic implementation in practice; and no proof of (ii) provides a closed-form characterization of Pareto optima. In addition, while all of the existing proofs of (i) are provided only for the case of a two-agent economy with the observation that they can be easily extended beyond two agents, such an extension is far from being trivial in the context of the algorithm of <span><span>Landsberger and Meilijson (1994)</span></span> and it has never been explicitly implemented. In this paper, we provide novel proofs of these foundational results. Our proof of (i) is based on the theory of majorization and an extension of a result of <span><span>Lorentz and Shimogaki (1968)</span></span>, which allows us to provide an explicit algorithmic construction that can be easily implemented beyond the case of two agents. In addition, our proof of (ii) leads to a crisp closed-form characterization of Pareto-optimal allocations in terms of <em>α</em>-quantiles (mixed quantiles). An application to peer-to-peer insurance, or collaborative insurance, illustrates the relevance of these results.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 1-16"},"PeriodicalIF":1.9,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662502","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

Automated machine learning in insurance 保险中的自动机器学习

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2024-11-08 DOI: 10.1016/j.insmatheco.2024.10.002

Panyi Dong, Zhiyu Quan

引用次数: 0

Pension funds with longevity risk: An optimal portfolio insurance approach 养老基金的长寿风险：最佳投资组合保险方法

IF 1.9 2区经济学

Insurance Mathematics & Economics Pub Date : 2024-11-01 DOI: 10.1016/j.insmatheco.2024.10.001

Marina Di Giacinto , Daniele Mancinelli , Mario Marino , Immacolata Oliva

{"title":"Pension funds with longevity risk: An optimal portfolio insurance approach","authors":"Marina Di Giacinto , Daniele Mancinelli , Mario Marino , Immacolata Oliva","doi":"10.1016/j.insmatheco.2024.10.001","DOIUrl":"10.1016/j.insmatheco.2024.10.001","url":null,"abstract":"<div><div>We present a unified framework designed to provide an optimal investment strategy for members of a defined contribution pension plan. Our model guarantees a minimum retirement savings level, expressed as a target annuity, by assuming uncertainty in interest rates, labor income, and mortality during the accumulation phase. To protect the accumulated retirement capital against both investment and longevity risks, the present value of the guaranteed lifetime annuity is regarded as the baseline wealth to hold upon reaching the retirement date, while a purpose-oriented proportion portfolio strategy is employed to invest the residual wealth. By applying standard dynamic programming techniques, we determine a closed-form solution to the stochastic control problem with the objective of maximizing the expected utility of the final surplus, defined as the difference between the accumulated wealth and the target annuity value. The theoretical findings are bolstered by a comprehensive numerical analysis designed to assess the impact of longevity on investment policies, highlighting the suitability of our proposal for managing defined contribution schemes.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"119 ","pages":"Pages 268-297"},"PeriodicalIF":1.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554230","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 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

Yuanying Guan , Muqiao Huang , Ruodu Wang

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

Roy Cerqueti , Arsen Palestini

{"title":"Bivariate Tail Conditional Co-Expectation for elliptical distributions","authors":"Roy Cerqueti , Arsen Palestini","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":"119 ","pages":"Pages 251-260"},"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

Jan Dhaene , Moshe A. Milevsky

{"title":"Egalitarian pooling and sharing of longevity risk a.k.a. can an administrator help skin the tontine cat?","authors":"Jan Dhaene , Moshe A. Milevsky","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":"119 ","pages":"Pages 238-250"},"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

Zongxia Liang , Yi Xia , Bin Zou

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

Yichun Chi , Tao Hu , Zhengtang Zhao , Jiakun Zheng

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

Yang Yang , Shaoying Chen , Zhenyu Cui , Zhimin Zhang

引用次数: 0