The Optimal Dividend Problem in the Continuous- Time Compound Binomial Model Under the Reinsurance Control

Yan Guo, Dingjie Fu

Abstract: In this paper, we study the optimal dividend problem in the continuous-time compound binomial model under the reinsurance control. For the first time, the continuous-time compound binomial model is proposed by the GX Wang, Y Lin, B Zhang, and the related theory of the continuous-time compound binomial model in the bankruptcy probability has been relatively mature. On this basis, First we introduce the concept of dividend and reinsurance, then discuss the optimal dividend problem of the continuous-time compound binomial model. This paper is divided into five parts the first part is preface, the second part modifies the continuous-time compound binomial model and introduce the definition of the restricted dividend. The third part discusses some properties of the value function. The forth part derives the HJB equation and the corresponding optimal dividend strategy, and proves that the solution which satisfy HJB is the value function. The fifth part is summary content.

Keywords: continuous-time compound binomial model restricted dividend under the reinsurance control HJB equation value function