保险公司最优投资和再保险策略

发布时间：2018-01-05 11:42

本文关键词：保险公司最优投资和再保险策略　出处：《燕山大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文利用随机理论、HJB方程、最优决策理论等数学工具，从保险中的风险问题出发，研究了最优投资和再保险策略。分别以理赔分布为指数分布和伽玛分布为前提，考虑再保险、风险投资及红利分配，利用动态模型方程对投资、再保险等问题进行合理分配，以期使破产时的期望红利达到最大。另外，利用动态模型方程求得了考虑超额损失再保险的情况下使破产概率最小策略的显式表达式。在跳-扩散风险模型的基础上，对于理赔为指数分布的情况下，引入非便宜比例再保险，投资有无风险资产和风险资产两种形式可供选择，并且当盈余达到分红标准时进行分红，使得破产时的期望红利最大，即找到最优的值函数（期望折现红利的最大值）。通过应用HJB方程理论得到最优投资策略和值函数满足的方程，再将其应用到指数形式的理赔分布中，求出有实际意义的最优投资策略显式解。算例中给出了一些参数对投资策略的影响，可以看出投资策略是符合实际情况的。在跳-扩散风险模型的基础上，对于理赔为伽玛分布的情况下，仅考虑投资和红利分配，投资有无风险资产和风险资产两种形式可供选择，并且当盈余达到分红标准时进行分红，使得破产时的期望红利最大，即找到最优的值函数（期望折现红利的最大值）。通过应用HJB方程理论得到最优投资策略和值函数满足的方程，再将其应用到伽玛形式的理赔分布中，求出有实际意义的最优投资策略显式解。算例中给出了一些参数对投资策略的影响，可以看出投资策略是符合实际情况的。在考虑再保险和投资的情况下使任意时刻破产概率最小，利用扩散逼近的方法，，通过求解对应的HJB方程得到了考虑超额损失再保险和投资策略及最小破产概率的最优策略的显式表达式。
[Abstract]:Based on stochastic theory , HJB equation , optimal decision theory and other mathematical tools , this paper studies the optimal investment and reinsurance policy from the risk problem in insurance . Based on the distribution of claims and the distribution of gamma distribution , the author considers reinsurance , venture capital and dividend distribution , and makes use of dynamic model equation to make rational distribution of investment and reinsurance . In addition , the explicit expression of the minimum policy of ruin probability is obtained by using the dynamic model equation . On the basis of the model of jump - diffusion risk , it is possible to introduce non - cheap proportional reinsurance , investment without risk assets and risk assets , and then apply the HJB equation theory to obtain the optimal value function ( the maximum value of expected discounted dividend ) . On the basis of the model of jump - diffusion risk , only the investment and dividend distribution , the existence of the risk assets and the risk assets are considered , and the best value function ( the maximum value of the expected discounted dividend ) is obtained when the surplus reaches the dividend criterion . The optimal investment strategy is obtained by applying the HJB equation theory . The effect of some parameters on the investment strategy is obtained . In consideration of reinsurance and investment , the ruin probability of any time is the least , and the explicit expression of the optimal strategy considering the excess loss reinsurance and the investment strategy and the minimum ruin probability is obtained by solving the corresponding HJB equation by solving the corresponding HJB equation .

【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F840.3

【参考文献】