扩散近似模型下的最优预防—再保险策略

Optimal Prevention-Reinsurance Strategies in Diffusion Approximation Risk Models

  • 摘要: 本文研究了扩散近似风险模型下的最优预防(干预)和比例再保险策略.保险公司使用两种策略管理索赔风险:购买比例再保险转移部分风险至再保险公司;单位时间投入资金p降低索赔强度λλ(p).在破产概率最小化目标下,利用随机控制理论和方法,论文建立相应的Hamilton-JacobiBellman (HJB)方程,从而解得最优预防-再保险策略和值函数.结果表明两种策略之间存在一定的关联性,都受到再保费安全附加系数和索赔均值大小的影响.简单来说,当再保险越贵时,保险公司更倾向于实施预防计划;反之,保险公司则对预防计划效果要求更高,因此更倾向于转移风险.我们还给出了相应的验证定理以及一个简单的数值算例.

     

    Abstract: In this paper, we investigate optimal prevention (intervention) and proportional reinsurance policies based on a diffusion approximation. The insurer chooses two strategies to control claim risk exposure: transferring risk to the third party by buying reinsurance; decreasing the intensity λ of claims to λ(p). Under minimising the probability of ruin, using ing techniques of stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman(HJB) equation and solve it to derive the optimal prevention-reinsurance strategy and value function. The results show there is a certain correlation between the two strategies, both of which are influenced by reinsurance premium claim size. Generally, as reinsurance becomes more expensive, insurance companies are more inclined to implement preventive plan; on the contrary, insurance companies have higher requirements for the effectiveness of prevention plan and are therefore more inclined to transfer risks by reinsurance. Verification and a numerical example are given to prove and illustrate our results.

     

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