Abstract

The Cramer-Lundberg's risk model has been studied for a long time. It describes the basic risk process of an insurance company. Many interesting practical problems have been solved with this model and under its simplifying assumptions. In particular, the uncertainty of the risk process comes from several elements: the intensity parameter, the claim severity and the premium rate. Establishing an efficient method to measure the risk of such process is meaningful to insurance companies.

Although several methods have been proposed, none of these can fully reflect the influence of each element of the risk process. In this thesis, we try to analyze this risk from different perspectives. First, we analyze the survival probability for an infinitesimal period, we derive a risk measure which only relies on the distribution of the claim severity. A second way is to compare the adjustment coefficient graphically. After that, we extend the method proposed by Loisel and Trufin (2014). And last, inspired by the concept of the shareholders' deficit, we construct a new risk measure based on solvency criteria that include all the above risk elements.

In Chapter 5, we make use of the risk measures derived in this thesis to solve the classical problem of optimal capital allocation. We see that the optimal allocation strategy can be set out by use of the Lagrange method. Some recent findings on such problems are also presented.