基于损失规避行为的带有错误定价和VaR约束的最优投资和再保险问题

黄晴,马世霞,李国柱

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (10) : 1790-1804.

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系统科学与数学 ›› 2020, Vol. 40 ›› Issue (10) : 1790-1804. DOI: 10.12341/jssms13981
论文

 基于损失规避行为的带有错误定价和VaR约束的最优投资和再保险问题

    黄晴,马世霞,李国柱
作者信息 +

The Optimal Investment and Reinsurance Problem with Mispricing and VaR Constrains Based on Behavior of Loss Aversion

    HUANG Qing, MA Shixia, LI Guozhu
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摘要

文章考虑了基于损失规避行为的带有错误定价和VaR约束的最优投资和再保险问题. 假设保险公司的的盈余过程遵循扩散模型, 允许保险公司购买比例再保险且在金融市场中投 资. 金融市场由无风险资产, 市场指数和一对错误定价的股票组成. 假定保险公司决策者是具有损失规避的非理性行为人, 并引入保险公司的VaR (Value-at-Risk)控制水平来控制其投资再保险策略的损失. 保险公司的决策目标是最大化最终财富的S型期望效用, 借助于鞅方法, 文章将动态的最优化问题转化为静 态最优化问题, 通过求解静态优化问题得到最优再保险和投资策略的解析表达式. 最后通过数值例子对最优 策略进行了敏感性分析.

Abstract

In this paper, we consider an optimal investment and reinsurance problem with mispricing and VaR constraints based on behavior of loss aversion. The insurer's surplus process is assumed to follow a diffusion model, and the insurer is allowed to purchase proportional reinsurance and invest in a financial market. The financial market consists of a risk-free asset, a market index, and a pair of mispriced stocks. The insurer's decision makers is assumed to have the non rational behavior of loss aversion, and we introduce the VaR (Value-at-Risk) control levels for the insurer to control its loss in investment-reinsurance strategy. The objective of the insurer is to maximize the expected utility of the S type of terminal wealth. With the help of martingale methods, we transform the dynamic maximization problem into a static optimization problem. By solving the static optimization problem, the explicit expressions for optimal investment and reinsurance strategy are obtained. Finally, the sensitivity analysis of the optimal strategy is carried out through numerical examples.

关键词

损失规避 / 投资与再保险 / 错误定价 / VaR约束 / 鞅方法.

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黄晴 , 马世霞 , 李国柱.  基于损失规避行为的带有错误定价和VaR约束的最优投资和再保险问题. 系统科学与数学, 2020, 40(10): 1790-1804. https://doi.org/10.12341/jssms13981
HUANG Qing , MA Shixia , LI Guozhu. The Optimal Investment and Reinsurance Problem with Mispricing and VaR Constrains Based on Behavior of Loss Aversion. Journal of Systems Science and Mathematical Sciences, 2020, 40(10): 1790-1804 https://doi.org/10.12341/jssms13981
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