| Now there are two common dividend strategies in the classical risk theory: one is barrier dividend strategy, which regards the overflow of the surplus as dividend when the surplus exceeds a fixed level b: the other is threshold dividend strategy, which paid overflow as dividend at a constant rate. With the development of risk theory, more and more risk models and theoretical methods are applied to analyze dividend problems. Albrecher et al.(2011a) have considered some dividend problems of the compound Poisson risk model when time interval of dividend have an exponential distribution. Therefore, we consider random barrier dividend strategy which share overflow as dividend at a random dividend time.In the classical risk theory, the insurance company has gone out of business when the surplus is below zero. But in the operation of insurance companies in the real world,company may continue doing business even if surplus is negative. The probability of bankruptcy depends on a function of the negative surplus ω(u). The notion of bankruptcy was first proposed by Albrecher et al. (2011b) to study the dividend problems when the surplus model is a Wiener process.In this paper, we consider two risk models’ random dividend oroblems under the frame-work of bankruptcy. This paper’s structure and content as fellows:Chapter 1 The notions of bankruptcy and random dividend and recent research progress.Chapter 2 We consider the random dividend problems of the compound Poisson risk model under bankruptcy. In section 2.1, the notion of the compound Poisson risk model and some symbols and definitions are introduced. In section 2.2, we deduce the integro-differential equations of the expected discounted dividends D(u, b) and solve the equations under some assumption. Then, We calculate some properties of D(b*,b*) and D’(b*,b*) after gainning the expression of optimal dividend barrier b* in section 2.3. In section 2.4, Some common bankruptcy rate function examples are given. Therefore, we discuss the piecewise bankrupt-cy rate functions to approximate the general bankruptcy rate function in section 2.5. In the final section, we use numerical simulation to verify and analysis previous conclusions.Chapter 3 We consider the random dividend problems of the compound Poisson risk mod-el perturbed by diffusion under bankruptcy. In section 3.1, we introduce the notion of the risk model and some symbols. With the similar method, we deduce the integro-differential equations of D(u,b) in section 3.2. In section 3.3, we derive the expression of D(u,b) under the conditions that claim amounts have an exponential distribution and ω(u) is a constant.Chapter 4 A brief summary of this dissertation is presented. |
