Research projects

Project CEMAPRE internal

TitleOptimal reinsurance with dependencies and applications
ParticipantsJoão Andrade e Silva, Alfredo Egídio dos Reis, Manuel Guerra, Alexandra Moura (Principal Investigator), Onofre Simões
SummaryThe project focuses on the optimal reinsurance of dependent risks, continuing the 2022 project
with the title "Optimal reinsurance with dependencies". In this 2023 Project we aim at continuing
studies which started in 2022, as well as to start new analysis and approaches. There are still open
questions regarding the optimal reinsurance problem with dependencies. Indeed, in spite optimal
reinsurance being a classical field of research in Actuarial Science, the inclusion of dependencies
makes it a very challenging subject of research. The interest in studying reinsurance under
dependencies is still increasing, driven by the need for real, robust and reliable quantitative risk
models, even though data is frequently very hard to obtain.

We will continue analysis that are already undergoing. Namely, we will proceed with the analysis of
the impact of Lipschitz constraints into the optimal reinsurance problem of general dependent risks,
characterizing of the optimal solutions, through necessary optimality conditions, and using it to
obtain numerical solutions in practical applications. We will continue to study the optimal
quota-share reinsurance minimizing the expected utility under a Cox-process, as well as the optimal
combinations of quota-share and excess of loss reinsurance minimizing the probability of ruin in a
diffusion process. We will carry on the analysis of the optimal surplus reinsurance treaty for a
real insurer portfolio.

We aim at analysing the reinsurance problem from both the insurer and the reinsurer view points, as
well as the reinsurance problem under dependencies related to catastrophic events.

Part of the work is planned to do in collaboration with researchers from international Universities,
such as Trondheim University, University of Lausanne and University of Amsterdam, or with
practitioners from Portuguese insurance companies.