Lundberg Upper Estimations For Ruin Probabilities In Some Types Of Continuous Time Risk Processess

In actuarial literature, compound Poisson risk model is the continuous time renewal riskprocess which has been studied extensively. In the present there are kinds of generalizationsof compound Poisson risk model, among these the compound compound Poisson risk model(abbreviated as CCPM) is proposed first by Minkova （Compound Compound Poisson RiskModel. Serdica Mathematical Journal,35,301-310,2009）, in which the related ruin problemsand reinsurance problems are studied. Motivated by the above mentioned paper, in this thesiswe suggest some new generalized CCPM and investigate the ruin probabilities in moredetails.In chapter1we introduce briefly the results for classical compound Poisson risk modeland CCPM, and some concepts of martingale and Brownian motion are reviewed. Chapter2deals with the CCPM with the premium process being another compound Poisson risk process.We first give the reasonable of the model and the explanations of the variables appeared in themodel. Then we get the explicit expression for the ultimate ruin probability, one example isalso presented. Based on chapter2, in chapter3we discuss the risk model proposed inprevious chapter but considering diffusion. After giving the structure of the model, we obtainthe Lundberg type inequality for the ultimate ruin probability. To be more applicable ininsurance practice, chapter four studies the ruin probability for the CCPM with the premiumprocess being double Poisson process. In the last chapter we further generalize the models,more precisely, we consider the CCPM with generalized compound compound Poissonprocess.In the proof s of the main results, we get the Lundberg type inequalities for the ruinprobabilities with three steps. Firstly, the positive safety loading is assumed for the insurancecompany. Secondly, for each surplus process {S t,t0}, we give the expression (r)suchthatE(e rSt) e (r)t, and prove the existence of the adjustment coefficient. In the last step,we obtain the upper estimation for the ruin probabilities by using of martingale technique.