Research projects

Project CEMAPRE internal

TitleReinsurance of dependent risks
ParticipantsMaria de Lourdes Centeno, Alexandra Moura (Principal Investigator)
SummaryThis 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.