The Research Of Discrete Time Risk Models With Dividend Strategy

Risk theory is theoretical foundation of quantitative analysis and forecasting risk. It provides the theoretical basis and practice guidance for management of insurance company. Dividend policy is an important means to enhance market competitiveness. And it can not only attract investment of shareholders but also attract policyholders. So the risk model with dividend policy becomes a popular subject for modern theory of risk to study. In this paper, we mainly further extend the existing three discrete time risk model, and establish the corresponding discrete time risk model with dividend policy. The main contents are as follows:1. Firstly, we study a discrete time risk model in a Markov environment with dividend policy. In every time interval, the claims’occurrences are described by a stationary Markov chain. The linear equations for the discounted penalty function of the model are derived; the relational expressions for the conditions of ruin probability, the probability function of the deficit at ruin and the surplus before ruin are obtained.2. We study the compound binomial model of dividend payments by using z transform. The z transforms of the ruin probability and the distribution of the surplus before ruin are obtained; We give two examples to explain the z inverse transform:the specific numerical of the ruin probability and the exact expressions of the distribution of the surplus before ruin are obtained by using a computer algorithm and the inversion of integral method respectively.3. We study the compound binomial model with special dividend strategy and stochastic premium income. Firstly, the recursive formulas for the discounted penalty function of the model are derived. And then the existence and uniqueness of solution to the equations are proved by applying some knowledge of matrix theory when the initial surplus is less than or equal to the threshold. Finally, the recursion formula respectively for ruin probability and the probability function of the severity of ruin are obtained.