arXiv subjects

Jose Luis Perez

Publications and source records attributed to Jose Luis Perez.

2 recordsLinked to original sources

arXiv2024

An optimal multibarrier strategy for a singular stochastic control problem with a state-dependent reward

We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish sufficient conditions for determining the optimality of the one-barrier strategy when the uncontrolled process $X$ follows a spectrally negative Lévy process with a Lévy measure defined by a completely monotone density. Secondly, to verify the optimality of the $(2n+1)$-barrier strategy when $X$ is a Brownian motion with a drift. Additionally, we provide an algorithm to compute the barrier values in the latter case.

math.OC↗

arXiv2015

Lévy insurance risk processes with parisian type severity of debt

In this article, we introduce a new definition of bankruptcy for a spectrally negative Lévy insurance risk process. More precisely, we study the Gerber-Shiu distribution for a ruin model where at each time the surplus goes negative, an independent negative random level is considered. If a negative excursion of the surplus exceeds such random level then the insurance company goes out of business. Our methodology uses excursion theory and relies on the description of the excursion measure away from 0 which was recently obtained by the authors in Pardo et al. (see arXiv:1507.05225). Our results are given in terms of the so-called scale functions.

math.PR↗