On Some Ruin Problem Of Cox Risk Model

This thesis mainly discuss the ruin quantities of Cox risk model with or without investment return. The first part (Chapter 2) of this thesis concentrates on the joint distributions of the surplus immediately before ruin, the deficit at ruin, the extreme surplus before ruin et al of Cox risk model by the idea presented in the work Wu Rong ([28], [37]) and the idea of time transform. In the second part of this paper (Chapter 3), Gerber-Shiu penalty functions for Cox risk model with con-stant interest force are studied, an system of integro-differential equations satisfied by the Gerber-Shiu functions and bounds for the Gerber-Shiu penalty functions are obtained. If the insurer can choose to invest in a risky market, we also give an optimal constant investment strategy by maximizing the adjustment coefficient within all constant investment strategies. It is shown that the optimal constant investment strategy is asymptotically optimal in the sense that " asymptotic dif-ference ", which means that when the initial surplus approaches to infinity, the optimal investment approaches to the optimal constant strategy we derived. This result is analogue to the one of Gaier et al ([12]).