Félix Locas | Searcharxiv

arXiv2024

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

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.

math.PR↗

arXiv2022

De Finetti's control problem with a concave bound on the control rate

We consider De Finetti's control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal. In order to solve this problem, we need to deal with a nonlinear Ornstein-Uhlenbeck process. Despite the level of generality of the bound imposed on the rate, an explicit expression for the value function is obtained up to the evaluation of two functions.This optimal control problem has those with control rates bounded by a constant and a linear function, respectively, as special cases.

math.OC↗