Multi-stage Dividend Model Of Classical Risk The Gerber-shiu Function

This dissertation is devoted to dealing with the Gerber-Shiu discounted penalty function (we will simply it to Gerber-Shiu function) on the compound Poisson risk model with several dividend rates, which includes the Gerber-Shiu function on the compound Poisson risk model with three dividend rates and the Gerber-Shiu function on the compound Poisson risk model with n+1 dividend rates.De.Finetti[l] first proposed dividend strategies for insurance risk models in 1957. Since then, the study of dividend strategies became increasingly important. See[2], [3], [4], [5]for detail. In[6], Gerber and Shiu introduced a discounted penalty function to analyze these related quantities in a unified manner. In[7], Lin and Willmot study the compound Poisson risk model with a barrier dividend strategy. In[8], Lin and Pavlova study the compound Poisson risk model with a threshold dividend strategy. Based on this, we apply the common application to study the Gerber-Shiu function on the compound Poisson risk model with three dividend rates firstly, and find the same between the Gerber-Shiu function on the compound Poisson risk model with three dividend rates and the Gerber-Shiu function on the compound Poisson risk model with two dividend rates, Which catch our attention. So we nextly study the Gerber-Shiu function on the compound Poisson risk model with n+1 dividend rates. In Chapter 1, a clear expression for the Gerber-Shiu function on the compound Poisson risk model with three dividend rates is given. Some important results are following:Theorem 1.3.1 Gerber-Shiu function m(u;b₁,b₂) satisfies Remark:Theorem 1.4.1 Gerber-Shiu function m₃(u) satisfiesConsidering the limitations of the compound Poisson risk model with three dividend rates, in Chapter 2, we study the compound Poisson risk model with n+1 dividend rates, Some important results are following: Theorem 2.2.1 Gerber-Shiu function m(u; b₁,…,b_n) satisfies the integro-differential equationsRemark:Theorem 2.3.1 Gerber-Shiu function m_n+1(u) satisfiesTheorem 2.3.2 Gerber-Shiu function m(u;b₁,…,b_n) satisfies...