CEV模型下时滞最优投资与再保险问题

doi:10.15960/j.cnki.issn.1007-6093.2020.01.006

摘要/Abstract

摘要： 在常方差弹性（constant elasticity of variance，CEV）模型下考虑了时滞最优投资与比例再保险问题.假设保险公司通过购买比例再保险对保险索赔风险进行管理，并将其财富投资于一个无风险资产和一个风险资产组成的金融市场，其中风险资产的价格过程服从常方差弹性模型.考虑与历史业绩相关的现金流量，保险公司的财富过程由一个时滞随机微分方程刻画，在负指数效用最大化的目标下求解了时滞最优投资与再保险控制问题，分别在投资与再保险和纯投资两种情形下得到最优策略和值函数的解析表达式.最后通过数值算例进一步说明主要参数对最优策略和值函数的影响.

关键词: 比例再保险, 常方差弹性(CEV)模型, 时滞随机微分方程, Hamilton-Jacobi-Bellman方程

Abstract: This paper considers the optimal investment-reinsurance problem with delay for an insurer under a constant elasticity of variance (CEV) model. Suppose that the insurer is allowed to purchase proportion reinsurance and invest her surplus in a financial market consisting of one risk-free asset and one risky asset whose price process is described by a CEV model. Under the consideration of the performance-related capital inflow/outflow, the wealth process of the insurer is modeled by a stochastic delay differential equation (SDDE). The objective of the insurer is to maximize the expected exponential utility of terminal wealth. The optimal strategies and the optimal value functions in the closed form are derived under two cases:the investment-reinsurance case and the investment-only case. Finally, some numerical examples and sensitivity analysis are provided for our results.

Key words: proportion reinsurance, CEV model, stochastic differential delay equation, Hamilton-Jacobi-Bellman equation

中图分类号:

阿春香, 邵仪. CEV模型下时滞最优投资与再保险问题[J]. 运筹学学报, 2020, 24(1): 73-87.

A Chunxiang, SHAO Yi. Optimal investment and reinsurance problem with delay under the CEV model[J]. Operations Research Transactions, 2020, 24(1): 73-87.

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