Optimality of refraction strategies for a constrained dividend problem
Optimization and Control
2026-01-14 v1
Abstract
We consider de Finetti's problem for spectrally one-sided L\'evy risk models with control strategies that are absolutely continuous with respect to the Lebesgue measure. Furthermore, we consider the version with a constraint on the time of ruin. To characterize the solution to the aforementioned models, we first solve the optimal dividend problem with a terminal value at ruin and show the optimality of threshold strategies. Next, we introduce the dual Lagrangian problem and show that the complementary slackness conditions are satisfied, characterizing the optimal Lagrange multiplier. Finally, we illustrate our findings with a series of numerical examples.
Cite
@article{arxiv.1803.08492,
title = {Optimality of refraction strategies for a constrained dividend problem},
author = {Mauricio Junca and Harold Moreno-Franco and José-Luis Pérez and Kazutoshi Yamazaki},
journal= {arXiv preprint arXiv:1803.08492},
year = {2026}
}