Study On Insurance Risk Under The Framework Of Web Markov Skeleton Process

Web Markov skeleton process (WMSP for short) is a new class of processes re-cently introduced by Ma’s group. Based on the work of Ma’s group, it is the first time this thesis introduces the notation of compound web Markov skeleton process (CWMSP for short), then it studies some insurance risk problems under the framework of web Markov skeleton process.As a hot area of research in risk theory, dependent risk is our focus in this paper. As a new class of processes, it applicable to model the dependence in risk theory, which will be a breakthrough in this area.Intuitively, a Markov skeleton process is a stochastic process employing a Markov chain as its skeleton. A web Markov skeleton process is a jump process and also a Markov skeleton process in which given information of its skeleton, the time slots between jumps are conditionally independent to each other. The system of a WMSP can be described as follows: where{Xn, n≥0} is a Markov chain, and{Tn, n≥0} is the set of time slots between adjacent jumps.A compound web Markov skeleton process (CWMSP for short) can be written as where Nt is the associated counting process, which denotes the number of jumps before t, and Yi is the accompaniment of ith jump, which is a r.v.. The system of a CWMSP can be described as follows:The system described by CWMSPs appear in various natural and social sciences, such as biology, finance, queueing theory, insurance and so on. In particular, CWMSP is a suitable framework for modeling the aggregate amount of claims when the claim sizes and inter-claim times are not independent.This thesis has five parts:The first part is the introduction and preliminaries, which are the main content of Chapter1. In the second part we introduce WMSP and CWMSP, and give the precise large deviation for CWMSP under some condition. And this part consists of Chapter2and3. The third part is Chapter4, which gives the precise large deviation for the aggregate amount of claims under some specified condition. The main topic of Chapter5,6and7is the discussion of the ruin problem under a given catastrophe risk model, which includes finite-time ruin probability and infinite time ruin probability. The last part is the conclusion and the future work.