The Compound Markov Binomial Model With Dividend Strategy

For a long time, the research of the dividend strategy on the risk models ofinsurance company focuses on the continuous-time models, however, the researchof the dividend strategy on discrete time risk models also has its value.In theformer research of the discrete time risk models, mainly in the compound binomialmodel, but its major drawback is to assume that the insurance company claimsare independent of each other, which is inconsistent with reality. In the real world,because of the common factors of risk business, in this paper, we assume that theclaim at any time happening or not are associated with its claims of a momentbefore, so as to introduce a Compound Markov binomial model, which can beseen as an extension of the compound binomial model, while taking into accountdividends paid on this model.In this paper, we mainly study the compound Markov binomial model withdividend strategy.In the first chapter, we introduce the background§current situation and thesignificance of this topic.In the second chapter, Consider a compound Markov binomial model witha constant dividend barrier. We derive the linear equations for the Gerber-Shiupenalty function and prove that the solution is unique. Finally, we give the solutionsfor some risk quantites as specific examples of the penalty function.In the third chapter, Consider the compound Markov binomial model withrandomized decisions on paying dividends. We derive the linear equations andrecursion formulas for the Gerber-Shiu penalty function. As specific examples ofthe penalty function, we discuss some risk quantites and give some correspondingresults.In the fourth chapter, we study the payments of dividends in the presence ofcompound Markov binomial model with a constant dividend barrier, we obtainedthe linear equations satisfying the expected present value of dividends,and derivethe approximate solution of the expected present value of dividends until ruin undera comparative condition.