Random Premium Income Of The Bankruptcy Of The Two-dimensional Risk Model

Risk theory is an important part in insurance mathematics, and ruin theory is the main content in risk theory. Lundberg-Cramer classical risk model is the first-emerging model in ruin theory. The contents of classical theory are deepened with people's com-prehensive and systematic research. For example, the risk model with random premium income is one of improved models. In this paper, a one-dimensional risk model with random premium income is extended to a two-dimensional risk model which is a two-dimensional risk model with random premium income. Of course, the two-dimensional risk model is not a simple extension of the one-dimensional risk model and it is more complicated than a one-dimensional model. In this thesis, we discuss the ruin problem of the two-dimensional risk model with stochastic premium through two methods.This thesis is divided into three chapters according to contents:Chapter 1 is prolegomenon, in which we mainly introduce the developmental history of risk model, the current situation of a two-dimensional risk model's research and part of interrelated knowledge of probability.In chapter 2, we discuss the ruin probability of a two-dimensional risk model with random premium income which is First, we obtain a Lundberg-type upper bound through the martingale technique. Then, by supposing that two kinds of premiums (C1j,C2j), j= 1,2,…and two kinds of claims (X1j,X2j), j= 1,2,…all obey ex-ponential distribution and their joint distribution functions F1(c1j,C2j),j= 1,2,…and F2(x1j,X2j),j= 1,2,…belong to bivariate Farlie-Gumbel-Morgenstern class, we analyse the upper bound's change of infinite-time ruin probabality by analysis of data when the correlation coefficientρ1 andρ2 change.In chapter 3, we mainly consider the ruin problem of the two-dimensional risk model through methods of the one-dimensional risk process. Firstly, we define a one-dimensional risk model where ai> 0,i= 1,2, and∑i=1 2 ai= 1.So the two-dimensional risk model defined in Chapter 2 is changed into the one-dimensional form Then we get the Lundberg inequality and the infinite-time ruin probability using some results of the one-dimensional risk process. Secondly, we obtain the integral equation of the Gerber-Shiu discounted penalty function fC(c1)fC(c2)…fC(cn)dc1dc2…dcn and the Laplace transform ofΦ(ua) if n = 1, which is Next, we verify that the result ofΦ(r) is consistent with the one-dimensional risk model's in special cases. Finally, we discuss the extended Gerber-Shiu discounted penalty function of the two-dimensional risk model with random premium income...