Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model
Optimization and Control
2018-09-10 v1 Portfolio Management
Abstract
Complementing existing results on minimal ruin probabilities, we minimize expected discounted penalty functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of optimal stochastic control and ultimately to the problem's Hamilton-Jacobi-Bellman equation. We show existence and uniqueness of the solution found by this method and provide numerical examples involving light and heavy tailed claims and also give a remark on the asymptotics.
Keywords
Cite
@article{arxiv.1809.00990,
title = {Optimal Reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model},
author = {Michael Preischl and Stefan Thonhauser},
journal= {arXiv preprint arXiv:1809.00990},
year = {2018}
}