风险相依状态下扩散逼近模型最优再保险问题
发布时间：2018-11-05 19:32
【摘要】：风险控制一直是保险公司的关键问题。在本文中,考虑一个保险公司的随机控制问题,并且求出保险公司再保险和投资的最优策略。该保险公司的盈余过程服从布朗运动。受到Browne (1995)工作的启发,该文章中理赔是连续的且是一个常数,我们对其模型进行拓展,加入两类状态相依的理赔项目,这两类理赔过程通过一个共同冲击联系起来。这使得模型更有说服力,并具有实际意义。通过一些技术处理,可以将一个连续的风险过程看作复合泊松模型的扩散逼近。在这一过程下,可以推导出模型到达预设上界的概率,并且能够得到值函数以及最优策略,包括保险公司再保险的自留份额以及投资风险资产的比例。通过对比之前的结论,发现最优策略不仅仅依赖于利率和盈余,而且还依赖于安全负荷。基于随机控制的理论,我们首先证明了扩散逼近模型的一些性质,之后提出了风险状态相依下的扩散逼近模型的验证定理。最后,根据两个具体的实例,求出具体的策略以及值函数。
[Abstract]:Risk control has always been a key issue for insurance companies. In this paper, we consider a stochastic control problem of an insurance company, and find out the optimal strategy of reinsurance and investment of insurance company. The insurance company's earnings process services from the Brownian motion. Inspired by the work of Browne (1995), claims in this paper are continuous and a constant. We extend the model and add two kinds of state-dependent claim items, which are connected by a common impact. This makes the model more convincing and has practical significance. Through some technical treatment, a continuous risk process can be regarded as the diffusion approximation of the compound Poisson model. In this process, the probability of the model reaching the preset upper bound can be derived, and the value function and the optimal strategy can be obtained, including the retention share of the reinsurance company and the proportion of the investment risk assets. By comparing the previous conclusions, we find that the optimal strategy depends not only on interest rate and earnings, but also on safety load. Based on the theory of stochastic control, we first prove some properties of diffusion approximation model, and then propose a verification theorem for diffusion approximation model with dependent risk state. Finally, according to two concrete examples, the concrete strategy and value function are obtained.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840.69
本文编号：2313148
[Abstract]:Risk control has always been a key issue for insurance companies. In this paper, we consider a stochastic control problem of an insurance company, and find out the optimal strategy of reinsurance and investment of insurance company. The insurance company's earnings process services from the Brownian motion. Inspired by the work of Browne (1995), claims in this paper are continuous and a constant. We extend the model and add two kinds of state-dependent claim items, which are connected by a common impact. This makes the model more convincing and has practical significance. Through some technical treatment, a continuous risk process can be regarded as the diffusion approximation of the compound Poisson model. In this process, the probability of the model reaching the preset upper bound can be derived, and the value function and the optimal strategy can be obtained, including the retention share of the reinsurance company and the proportion of the investment risk assets. By comparing the previous conclusions, we find that the optimal strategy depends not only on interest rate and earnings, but also on safety load. Based on the theory of stochastic control, we first prove some properties of diffusion approximation model, and then propose a verification theorem for diffusion approximation model with dependent risk state. Finally, according to two concrete examples, the concrete strategy and value function are obtained.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840.69
【参考文献】
相关期刊论文 前2条
1 杨潇潇;梁志彬;张彩斌;;基于时滞和多维相依风险模型的最优期望-方差比例再保险[J];中国科学:数学;2017年06期
2 ;Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion[J];Acta Mathematicae Applicatae Sinica;2007年03期
，本文编号：2313148
本文链接：https://www.wllwen.com/jingjilunwen/bxjjlw/2313148.html
