方差保费准则下的最优脉冲控制  

Optimal impulse control with variance premium principle

作　　者：孟辉[1] 

机构地区：[1]中央财经大学中国精算研究院,北京100081

出　　处：《中国科学：数学》2013年第9期925-939,共15页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11271385);教育部人文社会科学重点研究基地项目(批准号:12JJD790017和11JJD790004);中央财经大学科研创新团队支持计划资助项目

摘　　要：本文研究保险公司在有再保险控制下的最优脉冲分红问题.对保险公司的理赔损失,假定有两家再保险公司参与分保,且保险公司与两家再保险公司采取不同参数下的方差保费准则.进一步,假定保险公司有股东红利分配,且每次分红有固定交易费和比例税收,即脉冲分红.在扩散逼近模型下,本文应用随机动态规划方法研究破产前的最大期望折现分红,给出值函数的解析表达式,进而获得最优再保险策略和分红策略的具体形式.In this paper, we study the optimal impulse control problem with reinsurance strategy. We assume that two reinsurers participate in a reinsurance treaty for some loss, and the insurer and two reinsurers adopt the variance premium principle with different parameter respectively. Fhrther, we assume that the dividends are paid to shareholder of an insurance company, and every dividend payout incurs some fixed transaction costs and proportional taxes, i.e., impulse dividends. In diffusion model, we study the maximum of the expected discounted dividend payout until the time of ruin by dynamic programming approach, and closed-form solutions for the value function and optimal dividend-reinsurance strategy are obtained.

关 键 词：方差保费准则 再保险策略 脉冲分红 固定交易费Hamilton JACOBI Bellman（HJB）方程 

分 类 号：O212.1[理学—概率论与数理统计]