Optimality of a refraction strategy in the optimal dividends problem with absolutely continuous controls subject to Parisian ruin

2023/10/27 by Félix Locas, Locas, Félix, Jean‐François Renaud +1
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2310.18164

openalex publication_date 2023/10/27 · openalex created_date 2023/11/01 · openalex updated_date 2026/08/01

Abstract

We consider de Finetti's optimal dividends problem with absolutely continuous strategies in a spectrally negative Lévy model with Parisian ruin as the termination time. The problem considered is essentially a generalization of both the control problems considered by Kyprianou, Loeffen & Pérez (2012) and by Renaud (2019). Using the language of scale functions for Parisian fluctuation theory, and under the assumption that the density of the Lévy measure is completely monotone, we prove that a refraction dividend strategy is optimal and we characterize the optimal threshold. In particular, we study the effect of the rate of Parisian implementation delays on this optimal threshold.

Related

• Optimality of refraction strategies for a constrained dividend problem
• Optimal Dividend Control with Transaction Costs under Exponential Parisian Ruin for a Refracted Levy Risk Model
• Optimality of impulse control problem in refracted L 'evy model with\n Parisian ruin and transaction costs
• On the optimality of the refraction--reflection strategy for L 'evy\n processes
• On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models