Matteo Brachetta

Università degli Studi di Genova

Title

Optimal Self-Protection via BSDEs for Risk Models with Jump Clusters

Authors

Matteo Brachetta, Giorgia Callegaro, Claudia Ceci, and Carlo Sgarra

Abstract

In this talk we explore some recent advances in optimal control problems in Insurance Theory, with a special focus on self-protection strategies. This framework describes an insurance contract where the policyholder can choose both the level of protection, i.e. the covered losses, and the self-protection effort, which are the preventative actions taken to reduce the frequency of the claim arrivals. These strategies are assessed based on the utility maximization of the terminal wealth, incorporating a final reimbursement that can incentivize the buyer to increase her effort. We show that this problem can be formulated in terms of a suitable BSDE, for which we prove existence and uniqueness of the solution. Then, the optimal strategies are evaluated in terms of the BSDE solution.