Application Of Piecewise Deterministic Markov Processes To Risk Theory

The key point In analysis ofa risk model by martingale approach Is to construct a proper martingale．Dasslos and Embrechts(1989)indicated that PDMP theorypresented us a systematic toolkltto getthe neededmartingale．This dissertation Is devoted to the ruin theory for following three risk models In virtue of PDMP theory that was studied by Liu and Hou(2000)in detail． In Chapter 2,we discuss a risk model In which the costs of each claim and the epochofthe irstclalm all have geometrlcdlstrlbutlon．伙 computethe accurate value of＊thete ruin probability．In Chapter 3,we consider a risk model with dlvmends,wham was irst！ntroduced by Getoer．The expression ot the ruin probability Is obtained and It Is same as Gerber's．Moreover,we conslderthe boundaryofthe Infinite time rulnprobablllty and compute an example In which the costs of claim have gamma dlstrlbutlon G(a,2)．We also present an expression of＊thesion finite time ruin probability and give a relation between ruin probability and time of ruin when claim costs have exponentlal dlstrlbutlon．In Chapter 4,we consider a changeable premium model．This generalization Is based on the ldeaproposed by Granded that It Is natural to letthe safety loading at a time t be"small" lfthe risk business attains a large value at that time．We get its ruin probability and consider an example Indetall when claim costs have exponentlal dlstrlbutlon．...