2023/09/28 by Salvatore Federico, Giorgio Ferrari, Federico, Salvatore +3
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #49L20 #60G40 #91B30 #97M30 #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2309.16303
openalex publication_date 2023/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the insurance company evolves according to the diffusive approximation of the Cramér-Lundberg model, claims arrive at a fixed constant rate, and the distribution of their sizes is general. Furthermore, we do not specify any specific functional form of the retention level. The aim of the company is to take actions in order to minimize the sum of the expected value of the total discounted flow of capital injections needed to avoid bankruptcy and of the fixed activation cost of the reinsurance contract. We provide an explicit solution to this problem, which involves the resolution of a static nonlinear optimization problem and of an optimal stopping problem for a reflected diffusion. We then illustrate the theoretical results in the case of proportional and excess-of-loss reinsurance, by providing a numerical study of the dependency of the optimal solution with respect to the model's parameters.