Research On Period Problems For Pascal Dual Risk Model

In thesis, we mainly use probability and statistics, stochastic processes, combinatorial mathematics, matrix, and the theories and methods of economics, proceed from the dual model of compound Pascal risk model in insurance theory, combine the essence attribute of insurance with the basic characteristics of the insurance business, generalize compound Pascal risk model reasonably, and investigate problems related ruin time.Our research direction is mainly periodic problem. It can be roughly di-vided into two kinds, one is periodic observation, another is periodic dividend. The organization of this paper research is as follows.1. In the second chapter, we consider periodic observation and barrier div-idend policy based on the dual model of compound Pascal risk model, and a dual compound Pascal risk model with periodic observation and dividend is es-tablished. The explanation that is we can only observe the surplus of insurance company at periodic time and the definition of ruin time is changed, is provid-ed. The Gerber-Shiu function and expected total discounted dividend before ruin time is studied, and the calculation method and the explicit expression are derived, respectively. Also, through specific numerical example, we analysis the influence of periodic observation on the expected total discounted dividend before ruin time.2. In the third chapter, based on the dual model of compound Pascal risk model, we consider periodic barrier dividend policy, and a dual compound Pascal risk model with periodic dividend is established. The insurance company can only consider the dividend at periodic time, and do not consider it in other time. The expected total discounted dividend before ruin time is studied, and the explicit expression is derived by contracting mapping principle. Moreover, the moment of total discounted dividend before ruin time is discussed and the expression is obtained.We discuss a periodic problem from two different angles,and we finally get the expressions of our targets by using two different methods. According to the conclusion obtained in this paper, the operation of insurance company has a certain degree of guidance and early warning role.