Abstracts

The optimal reinsurance problem and the dividendproblem are concerned in this thesis for some risk models withdependence. Specifically, the models of our study consist ofmultiple classes of insurance business which are correlated due tothe so-called thinning-dependence structure. In the first part,we study the optimal reinsurance problem based on a continuous-timerisk model with thinning dependence for two typical reinsurancepremium principles, namely the expected value premium principle andthe variance premium principle. The optimal reinsurance strategiesare derived under the criterion of maximizing the adjustmentcoefficient or minimizing the well-known Lundberg upper bound forthe ruin probability. Numerical examples are also provided toillustrate the impact of the model parameters on the optimalreinsurance strategies. In the second part, we consider theexpected discounted dividends until ruin for a discrete-time riskmodel with thinning dependence, where dividends are paid accordingto a barrier strategy. Under a barrier strategy, when the surplusof each class is above a certain barrier level, the excess part ispaid immediately as dividends. To compute the expected discounteddividends for each class, we need to consider the vector of theclaim-size random variables from all classes and derive their jointprobability mass function. With the help of the multivariate Panjerrecursion for the joint probability mass function of the claimsizes, several equations related to the expected discounteddividends are obtained according to the levels of initial capital.The common shock structure is discussed as a special case and thecorresponding equations are derived. We also carry out somenumerical examples to show the impact of model parameters on thedividend payments. published_or_final_version Statistics and Actuarial Science Master Master of Philosophy