Periodic Dividend Analysis Of A Sparse Risk Model For A Class Of Dependent Structures

The classical risk model charges a, premium with constant rate, but in the real operation of insurance company, premium income is random. At the same time, it is usually related to claim happened. Therefore, this paper considers the dependency structure of thinning risk model. In this model, assuming that arrival process of the policy is Poisson process and its parameter is ?. At the same time arrival process of claims is a P-thinning process.Gerber and Shiu (1998) first proposed Gerber - Shui function(also known as the expected discounted penalty function). The paper provides a unified method ,which can solve multiple actuarial amount. De Finetti (1957) first put forward the problem of sharing out bonus, and in the current problem of sharing out bonus is a hot, research topic. This paper consideres a class of thinning sisk model and studies the expected discounted penalty function and expected discounted cumulative dividends function under the periodic dividend policy. The integral equation that they respectively satisfied is obtained. Meanwhile I also obtained the specific expression under the special circumstances and the exact expression of the ruin probability.The first chapter is the introduction, introducing a sparse risk model with dependent structure and the background and status quo of periodic dividend strategies.The second chapter is to prepare knowledge and to introduce model. And the chapter focuses on sparse risk model and periodic dividend strategies. And it also introduces basic concepts such as Gerber - Shiu function.The third chapter and the fourth chapter contain the main research results in this paper.In the third chapter, I got the integral equation for the expected discounted penalty function under periodic dividend strategies. The integral equation is that,when 0 ? u ? b .In this chapter, when the amount of claim and premium are subject to exponential distribu-tion, I obtained the explicit expression of the expected discounted penalty function at the same time. The explicit expression is thatFinally, the closed expression of ruin probability is obtained. The closed expression is that.In the fourth chapterr,we study the integral equation for the expected discounted cu-mulative dividend funetion of the sparse risk model with periodic dividend policies. The integral equation is that when 0 ? u ? b,At, the same time, I got the specific expression of the expected discounted cumulative divi-dend function when the amount of claim and premium are subject to exponential distribu-tion.The fifth chapter makes a summary of this paper.