The Study Of Dividends And Bankruptcy In The Compound Binomial Risk Model With Dividend Strategies

This thesis studies some issues from the perspective of dividend distribution policy.This paper mainly considers two kinds of Dividend Strategies of the risk theory based on the compound binomial risk model.One is the constant divi-dend barrier strategy and the other is multi-threshold strategy(threshold strat-egy).Based on the compound binomial model we consider dividend model which is more complex and more closer to the reality. Meanwhile we set multi-threshold strategy or(dividend barrier) and then introduce the payment of dividend of ran-domization policy program.finally we construct a random payment of dividend of multi-threshold strategy based on the compound binomial model.The surplus model considered in this article not only contents the requirement for insurance companies to boost earnings but also take into account the interests of policy hold-ers at the same time.This paper aims to solve dividends and bankruptcy issues for the compound binomial risk model with a dividend strategy and use the con-traction mapping and fixed point theorem to solve three types of risk model with a dividend strategy.We hope to provide insurance companies with the design and management of insurance dividends and a corresponding theoretical basis.In the discrete-time model, the optimal dividend problem is few involved issues studied of risk theory.So it can be regarded as an issue of great research value.Under the work of many predecessors this paper not only provides a more widespread practical mathematical methods but also get the renewal equation for the Gerber-shiu discounted penalty function as well as the expected present value of dividends according to all types of dividend model.Furtherly we get the kth moment of the expected present value of dividends.Studying on these issues can provide strong theoretical reference for the improve of risk management of insurance companies.The first chapter describes the study process of the dividend strategy risk model in history and the present status,and meanwhile describes the research background of the problem.Chapter II study constant barrier strategy in the compound binomial risk model.We get the flowing result,such as the expression of the expected present value and kth moment of dividend,the total dividend distribution type without discount,the expected discounted Gerber-shiu penalty function and some other important risk amount of dividends.In the solution,we used two methods to study the expected present value of dividend.The first one is based on the time when the first claim happens.The other is based on the first unit one.Chapterâ…¢consider a model of random payment of dividend.By using two recursive equations given by others we obtain two renewal equation and corre-sponding analytical solution of Gerber-shiu discounted penalty function.Using the analytical solution we get the final probability of bankruptcy, insolvency deficit and the surplus just before bankruptcy.This chapter also takes into account the asymptotic estimation for the penalty function.As a promotion we get recursion equations and the renewal equations satisfied by the penalty function with a dis-count.Then we consider a dual-threshold model of random dividend payments and get the expected present value of dividends under this model.The fourth chapter consider another dual-threshold model of dividend pay-ments based on the promotion of the compound binomial surplus model(ie the premium is a constant c).Iterative method has also been used in this model and obtain the expected present value of dividends.