Research projects

Project CEMAPRE internal

TitleOptimal Reinsurance of Dependent Risks with Applications
ParticipantsJoão Andrade e Silva, Alfredo Egídio dos Reis, Manuel Guerra, Alexandra Moura (Principal Investigator), Carlos Oliveira
SummaryThe 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.