带技术投资的保险公司最优策略

The optimal policy for insurance company with technology investment

中文关键词  破产概率  混合随机决策–最优停时问题  比例再保险  变分不等式

英文关键词  ruin probability  mixed stochastic control/optimal stopping problem  proportional reinsurance  variational inequalities

中文摘要

      本文站在保险公司的角度, 假定1) 保险公司采用连续比例再保险的方式将自身的部分风险转移到再保险公司, 2) 保险公司可以选择在某一时刻进行项目投资, 该投资不直接产生收益, 但可以降低公司所面临的风险. 本文的目标是通过选择最佳投资时刻和最优再保险比例来最小化破产概率. 运用混合随机决策–最优停时方法, 本文求解出破产概率和最优再保险策略的显式表达式以及最佳投资时刻的半显式解. 作为本文结果的一个应用, 本文以数值模拟的方式揭示了投资效果, 投资金额和最佳投资时刻3者之间的关系: 1) 投资总是可以降低破产概率; 2) 投资效果越明显, 投资所需金额越小, 则应该选择尽早投资; 反之则应该推迟投资时间, 等积累到足够的资金再进行投资.

英文摘要

      From the view point of an insurer, one assumes that 1) the insurance company’s risk is reduced through proportional reinsurance; 2) the company may invest a fixed amount of money in new technology to reduce its risk as return. The object of this work is to minimize the ruin probability for the company and to seek the corresponding optimal strategy. Using the methodology of mixed stochastic control/optimal stopping, we find the quasi-explicit expression for the minimal ruin probability as well as the optimal investing time-reinsurance policy. Some numerical results are given to illustrate the inter relationship among the investment effect, investing amount and optimal investing time. The numerical results show that: 1) Investment is effective in reducing minimal ruin probability; 2) Less investing amount and better investing effect imply earlier investing time. Otherwise, it is optimal to postpone the investment until the surplus is sufficient.