Project CEMAPRE internal
| Title | Reinsurance of dependent risks |
| Participants | Maria de Lourdes Centeno, Alexandra Moura (Principal Investigator) |
| Summary | This work focuses on the study of the optimal levels of retention for an insurance company intending to reinsure two dependent risks. Little can be found in literature regarding reinsurance retention limits of dependent risks. In Centeno (2004, Dependent risks and excess of loss insurance) dependence is considered in the number of claims only, and not in the severity of the claims. In Cai and Wei (2012, Optimal reinsurance with positively dependent risks) the authors analyze this problem considering the expected value principle and defining positive dependence through the stochastic ordering. The authors demonstrate the result by exploiting the convex order of the stochastic ordering and considering the maximization of the expected utility as optimality criterion. In this project, we aim at extending Cai and Wei result to the case of the variance related premium calculation principles, which have already been analyzed in Guerra and Centeno (2010, Optimal reinsurance for variance related premium calculation principles), but for independent risks. We also intent to follow a different methodology, by accounting for dependence through the definition of copulas. Copulas are widely used in risk management, namely in actuarial sciences, and are particularly interesting as they provide expressions for the joint probability function of dependent random variables. Nevertheless, in spite this fact, the complexity of dependent risks makes it very difficult to obtain a theoretical optimal retention level result in this case, even for the expected value principle. For this reason, we will apply Numerical Analysis to solve this problem. Although this approach will not permit to obtain theoretical results, it will allow to consider a wider range of scenarios, as for instance different premium calculation principles and optimality criteria. |