Research projects

Project CEMAPRE internal

TitleOptimal Reinsurance of Dependent Risks
ParticipantsMaria de Lourdes Centeno, 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.

The aim of the project is twofold: i) (continuation of the 2019 internal project) to obtain
optimality conditions of risk transfer for an insurance company willing to reinsure two dependent
risks, generally considering dependence through the joint distribution, using several premium
principles and optimality criteria; ii) 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.

We will account for reinsurance premium loadings including the expected value principle, but also
variance related premium loadings and possibly other premium principles. Several optimality criteria
will also be considered, including the analysis of the probability of ruin.

The complexity introduced in the optimization problem by the dependencies leads to the need of
numerical methods in most situations. We will consider both numerical and analytical approaches.
Specially at the numerical level, copulas will be a preferential framework to obtain explicit
solutions and examples.