Study On Two Dependent Risk Models

This thesis studies two dependent risk models in which the premium rate is not a fixed constant. The first type is a time-dependent premium risk model in which premium rates are adjusted continuously according to the current level of an insurer's surplus. When surplus r(?)υ, the premium rate c(r)=c1+εr and when surplus r>υ, the premium rate c(r)=C2+εr, where c1, c2,εand r are all constants. We obtain expression for the ruin probability. For the exponential claim sizes, we exactly solve the ruin probability step-by-step. the second type is a Markov-dependent risk model in which the premium rate, the claim amounts and the interclaim time are depended by an irreducible discrete-time Markov chain. Based on the analysis of the discounted penalty function by means of Laplace-Stieltjes transforms, we drive moments of three characteristics of the ruin process. A renewal model with generalized Erlang(n)-interclaim times is contained as a special case.