Research On The Periodic Dividend Strategy In The Dual Risk Model

Since De Finetti(1957)put forward the dividend problem in discrete time risk model,the dividend problem has been widely concerned in actuarial.Many scholars have studied the dividend problem in the classical risk model.The classical risk model describes the surplus process of insurance companies.However,some research-based and task-based companies have random income,and their surplus processes are described by dual risk.The dividend problem is considered under two cases:continuous and discrete inter-dividend time.The discrete time dividend is more realistic.This thesis considers the discrete time dividend problem in the dual risk model.The main contents of this thesis are as follows.In chapter 2,we assume that the dividend time interval is exponential,and consider the optimal periodic dividend problem with capital injection and ruin penalty.First,we divide the original optimal problem into two suboptimal problems:without capital injection and forced capital injection to prevent ruin.We give a comparison theorem and prove that a periodic dividend barrier is optimal under some conditions.The expression of the value function and the optimal dividend barrier are given when the income jumps follow a hyper-exponential distribution,and some numerical examples arc given to analyse the effect of ruin penalty on the barrier of periodic dividend and the value function.In Chapter 3,we study the problem of periodic dividend when time interval of dividend distribute Erlang(2).We first give the expected value of dividend discount functions before ruin when the periodic dividend barrier is b=0.For b>0,we get the expected present value of dividends discount functions before ruin by special linear combination of exponential functions.