基于损失规避行为的最优保险投资与再保策略选择

郭文旌

系统科学与数学 ›› 2018, Vol. 38 ›› Issue (9) : 1005-1017.

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PDF(499 KB)
系统科学与数学 ›› 2018, Vol. 38 ›› Issue (9) : 1005-1017. DOI: 10.12341/jssms13434
论文

基于损失规避行为的最优保险投资与再保策略选择

    郭文旌
作者信息 +

Optimal Investment and Reinsurance Strategy Selection Based on Behavior of Loss Aversion

    GUO Wenjing
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文章历史 +

摘要

保险公司决策者一方面通过投资来实现保险资金的保值增值, 另一方面通过再保险业务来控制承 保风险. 保险投资市场假定是由两种资产构成: 一种是无风险资产, 另一种是风险资产. 与已有研究不同, 文章基于累积前景理论, 假定保险公司决策者具有损失规避异质性的非理性行为人. 保险公司的盈余过程用跳跃扩散过程来刻画, 保险公司的决策目标是最大化最终财富的``S"型期望效用, 借助于鞅理论将动态的最大化问题转化为静态问题, 通过求解静态优化问题得到了最优投资和再保险策略的解析表达式. 数值模拟分析了最优策略的动态性质.

Abstract

Insurance company decision makers on the one hand invest to achieve the value of insurance funds, on the other hand carry out reinsurance business to control underwriting risk. Insurance investment market is assumed to be made up of two types of assets: One is a risk-free asset, the other is a risk asset. Different from existing research, this paper assumes that insurance company decision makers have the non rational behavior of loss aversion based on CPT. The surplus of the insurance company is described by jump diffusion process. The objective of the insurance company is to maximize the expected utility of the ``S" type of terminal wealth. With the help of martingale theory, the dynamic maximization problem is transformed into a static optimization problem. By solving the static optimization problem, the explicit expressions for optimal investment and reinsurance strategy are obtained. The dynamic properties of the optimal strategy are analyzed by numerical simulation.

关键词

损失规避 / 保险投资 / 再保险 / 跳跃扩散过程 / 鞅.

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郭文旌. 基于损失规避行为的最优保险投资与再保策略选择. 系统科学与数学, 2018, 38(9): 1005-1017. https://doi.org/10.12341/jssms13434
GUO Wenjing. Optimal Investment and Reinsurance Strategy Selection Based on Behavior of Loss Aversion. Journal of Systems Science and Mathematical Sciences, 2018, 38(9): 1005-1017 https://doi.org/10.12341/jssms13434
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