Survival probability and ruin probability of a risk model

Abstract

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special case-exponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.

On the Expected Discounted Penalty Function for a Risk Model with Thinning Process

“…Many results on ruin probability have been obtained, see, e.g., [1][2][3][4][5], and so on. In [6], Luo generalized the classical risk model to the case where the arrival of insurance policies is a Poisson process and the process of claim occurring is a p-thinning process. The integral representations on the survival probability is discussed and its explicit formula on the infinite interval is obtained in the special case--exponential distribution.…”

“…T T In this paper, we firstly introduce the risk model considered as in [6], then derive integral equation satisfied by the discounted penalty function. But in traditional study, the discount interest force is often assumed to be constant.…”

“…Remark 3.1. If ( , ) 1 w x y = and ( ) 0 r t = in (9), denoting non-ruin probability 0[6] is a special case of Theorem 3.1 in this paper. Remark If ( , ) 1 w x y = and ( ) 0 r t = in (9), denoting ruin probability ( ) 1 ( )…”