Project CEMAPRE internal
| Title | Optimal Reinsurance of Dependent Risks with Applications |
| Participants | João Andrade e Silva, Alfredo Egídio dos Reis, Manuel Guerra, Alexandra Moura (Principal Investigator), Carlos Oliveira |
| Summary | The work focuses on the optimal reinsurance of dependent risks. While a large quantity of studies can be found in literature concerning optimal reinsurance strategies, only recently dependence has been considered and very few works can be found on the optimal reinsurance of dependent risks through the claim severity, specially if premium loadings other than the expected value principle are considered. The interest in studying optimal reinsurance under dependencies is increasing, driven by the need for real, robust and reliable quantitative risk models. Optimality conditions of risk transfer for an insurance company willing to reinsure n dependent risks were found, for general dependence through the joint distribution, using several premium principles and maximizing the expected utility as optimality criteria. We aim now at analysing the implications of constraints such as the usual moral hazard constraint. We also aim to grapple the optimal reinsurance problem using optimal control of discrete dynamical processes. Many authors consider continuous dynamical processes, namely continuous diffusion processes, when describing the optimal reinsurance problem. In particular, they assume that reinsurance can be bought and sold at any time instante. However, in practical context, reinsurance contracts are valid for a fixed period of time (usually one year), so in this work discrete dynamical processes will be considered. The complexity introduced in the optimization problem by the dependencies leads to the need of numerical methods in most situations. The project will also focus on the numerical applicability of the theoretical results. Namely, applications to data will be addressed, using the copula framework. |