跳跃盈余下的保险最优投资

Optimal investment with jump surplus for insurers

假设保险公司的盈余过程为纯跳跃的Cramer-Lundberg模型,投资市场是由一个无风险资产和n个风险资产构成的资本市场.考虑一个有限时间区间的最优投资策略选择问题——最小化保险公司的实际财富的终期值与公司预期值的偏差,利用LQ随机控制方法得到了保险公司的最优组合投资策略的解析表达式以及保险公司投资的有效投资边界的显式表达式,分析了保费率与索赔过程对最优投资策略的影响.

Under the assumptions that the surplus process is a Cramer-Lundberg model with pure jumps and that the investment market is made up of one risk-free asset and n risk assets, an optimal portfolio selection problem of a finite time interval is investigated, for the purpose of optimizing the warp between the terminal wealth and expected wealth. The LQ stochastic control method was applied to get the explicit form of the optimal investment strategies and the efficient frontier in a closed form. Effects of premium and claim on optimal investment strategies was analyzed.