Optimal Moral-Hazard-Free Reinsurance Under Extended Distortion Premium Principles

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-05-13 DOI:10.1137/23m1556046

Zhuo Jin, Zuo Quan Xu, Bin Zou

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1390-1416, June 2024.
Abstract. We study an optimal reinsurance problem under a diffusion risk model for an insurer who aims to minimize the probability of lifetime ruin. To rule out moral hazard issues, we only consider moral-hazard-free reinsurance contracts by imposing the incentive compatibility constraint on indemnity functions. The reinsurance premium is calculated under an extended distortion premium principle, in which the distortion function is not necessarily concave or continuous. We first show that an optimal reinsurance contract always exists and then derive two sufficient and necessary conditions to characterize it. Due to the presence of the incentive compatibility constraint and the nonconcavity of the distortion, the optimal contract is obtained as a solution to a double obstacle problem. At last, we apply the general result to study four examples and obtain the optimal contract in (semi-)closed form.

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扩展扭曲溢价原则下的最优无道德风险再保险

SIAM 控制与优化期刊》第 62 卷第 3 期第 1390-1416 页，2024 年 6 月。摘要。我们研究了一个扩散风险模型下的最优再保险问题，该问题的目标是使保险人终生破产的概率最小化。为了排除道德风险问题，我们只考虑无道德风险的再保险合同，对赔偿函数施加激励相容约束。再保险费根据扩展的扭曲保险费原则计算，其中扭曲函数不一定是凹形或连续的。我们首先证明最优再保险合同总是存在的，然后推导出两个充分必要条件来描述最优再保险合同。由于存在激励相容约束和扭曲的非凹性，最优合同可以作为双重障碍问题的解而得到。最后，我们运用一般结果研究了四个实例，并得到了（半）封闭形式的最优合同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.