2021/09/29 by Josef Anton Strini, Strini, Josef Anton, Stefan Thonhauser +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2109.14373
openalex publication_date 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the dividends and the penalty, which causes time-inconsistency. This allows to study different types of constraints. For the diffusion approximation of the classical surplus process we derive an explicit equilibrium dividend strategy and the associated value function. Inspired by duality arguments, we can identify a particular equilibrium strategy such that for a given initial surplus the imposed constraint is fulfilled. Furthermore, we illustrate our findings with a numerical example.