相依索赔下受VaR及政策约束的最优保险投资

Optimal Insurance Investment with Dependent Claims under the Constraints of VaR and Policy

在索赔风险两两拟渐近独立且正则变化尾的假定下,以VaR度量整体风险(承保风险和投资风险),兼顾政策约束,研究最优保险投资问题.以终期期望财富最大为目标,利用破产概率的渐近结果得到了近似的最优策略,并结合数值案例进行了模拟分析.结果表明:由于相依风险的复杂性,在最优策略的求解条件中,需明确限定索赔重尾指数;当保险公司合理设置风险水平时,最优策略可以最大化终期期望财富;在风险水平设置偏高时,监管比例可以有效地控制风险.

To optimize insurance investment for an insurer with pairwise quasi-asymptotic independent and regularly-varying-tailed claims,where the integrated risks（underwriting risks and investment risks） were measured by VaR and policy constraint was considered.Under the goal of maximizing the terminal expected wealth,asymptotic strategies were obtained by applying the result of asymptotic ruin probability,and analysis was given combining with numerical simulation.The results show that,due to the complexity of dependent risks,the heavy-tailed index need be explicitly limited in the conditions for solving optimal strategies;the optimal strategies can maximize the terminal expected wealth when the insure sets appropriate risk levels;the ratio of supervision can control risks effectively when the risk level is set too high.