Research On Optimal Control Towards The Joint Reinsurer Sides With Dependent Risk Model

With the development of the insurance finance industry,how to choose the best business strategy to achieve the desired business objectives has become a hot topic in the insurance actuarial field.Random control theory can be said to be tailored for these issues theory.However these problems in turn promote the development of stochastic control theory.Therefore,random control theory plays an important role in insurance application.Recently,as the stochastic control theory research gradually in-depth,more and more practical models are taken into account the insurance financial prob-lems in order to better choose the best business strategy to achieve the expected business objectives,such as threshold dividend model,dependent risk model,joint interests,and so on.The paper investigates the optimal control problem for joint interests of the insurer and reinsurer with dependent risks by the stochastic process,Markov process,stochastic control theory and risk theory.We study two kinds risk model:the compound poisson and diffusion approximation risk models.The paper's main ideas as follows:portfolio selection aims to seek a best asset allocation which maximizes the terminal profit or minimizes the risk.The chapter 3,we briefly introduce the research background and meaning of the risk theory.Usually,optimization objective function of the joint optimal investment-reinsurance problem is set up through maximizing the expected u-tility of terminal weighted sum surplus process which is took into account the interests of both the insurer and the reinsurer.The chapter 4,under the criterion of maximizing the expected exponen-tial utility with the variance premium principle,and both the insurer and the reinsurer are assumed to invest in a risky asset,which is distinct for each other and driven by a constant elasticity of variance model.We adopt a nonstandard approach to examining the existence and uniqueness of the optimal reinsur-ance strategy.Using the technique of stochastic control theory,closed-form expressions for the optimal strategy and the value function are derived for the compound Poisson risk model as well as for the Brownian motion risk model.From the numerical examples,we see that the optimal results for the compound Poisson risk model are very different from those for the diffusion model.The chapter 5,a proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle.We adopt a nonstandard approach to examining the existence and uniqueness of the optimal reinsurance strategy.