2024/09/19 by Zakaria Aljaberi, Aljaberi, Zakaria, Asma Khedher +3
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2409.12523
openalex publication_date 2024/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in which capital injections are allowed. Our aim is to find a general dynamic reinsurance strategy that maximises the expected discounted cumulative dividends until the time of passage below a given level, called ruin. These policies consist in stopping at the first time when the size of the overshoot below 0 exceeds a certain limit a, and only pay dividends when the reserve reaches an upper barrier b. Using analytical methods, we identify the value function as a particular solution to the associated Hamilton Jacobi Bellman equation. This approach leads to an exhaustive and explicit characterisation of optimal policy. The proportional reinsurance is given via comprehensive structure equations. Furthermore we give some examples illustrating the applicability of this method for proportional reinsurance treaties.