Ruin Probability In Finite Horizon Of A Discrete-time Model Under The Periodic Factors Of Weather

The main task of this paper is to study the ruin probability of a finite discrete-time model with two kinds of financial risks. It includes 5 chapters and the main contents are as follows:Chapter 1 is the introduction of this paper which introduces the problem of ruin probability, the present state of research in and abroad, the basic idea of the ruin theory, the aim and meaning of this paper, heavy tailed distributions and their properties etc.Chapter 2 is the backgrounds of this paper. It introduces the half-year net income, half-year investment pattern and so on of an insurance company, defines the symbols used in the paper, gives some explanations and brings forward the concept of surplus process. The ruin model used in our paper is also given in this chapter. The end of this chapter introduces the achievement and innovation of the paper. Chapter 3 studies the ruin probability within an odd number of half-years of an insurance company. Theorem 3.1 gives the asymptotic formula for ruin probability within an odd number of half-years. The proof of it uses the properties of uniform convergence, the conclusions of weighted sums of random variables, the properties of heavy tailed distributions etc. Chapter 4 studies the ruin probability within an even number of half-years. Theorem 4.1 gives the asymptotic formula of the probability The proof of it uses the properties of uniform convergence, the conclusions of randomly weighted sums of random variables and so on. Chapter 5 gives two corollaries. The conditions in this section are the special cases in the preceding 2 chapters. Corollary 5.1 and corollary 5.2 give the asymptomatic ruin probability formulas within an odd as well as an even number of half-years. The proofs of them use the conclusions in theorem 3.1 and 4.1.The 6th chapter is the summary of the whole paper, and it offers some proposals for the future study.