In this thesis we investigate the ruin probability in the classical risk model. Let F_e be the distribution of the claim size belongs to S(γ),γ ≥ 0.We derive the asymptotic relationship by the geometric sum method,where This thesis consists of three chapters as follows.In Chapter l,we introduce many results about ruin probability;in Chapter 2, we Introduce some relative tail distribution classes and their property; in Chapter 3,we give the main result and prove it.
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