arXiv subjects

Harold Moreno-Franco

Publications and source records attributed to Harold Moreno-Franco.

4 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↗

arXiv2018

Optimal bail-out dividends problem with transaction cost and capital injection constraint

We consider the bail-out optimal dividend problem under fixed transaction costs for a Lévy risk model. Furthermore, we consider the version with a constraint expected net present value of injected capital. To characterize the solution to the aforementioned models, we first solve the bail-out optimal dividend problem under transaction costs and capital injection and show the optimality of reflected (c1; c2)- policies. 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.

math.PR↗

arXiv2018

Optimality of refraction strategies for a constrained dividend problem

We consider de Finetti's problem for spectrally one-sided Lévy 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.

math.OC↗

arXiv2017

A time of ruin constrained optimal dividend problem for spectrally one-sided Lévy processes

We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We extend the results in \cite{HJ15}, now in context of one-sided Lévy risk models. We consider de Finetti's problem in both scenarios with and without fix transaction costs, e.g. taxes. We also study the constrained analog to the so called Dual model. To characterize the solution to the aforementioned models we introduce the dual problem and show that the complementary slackness conditions are satisfied and therefore there is no duality gap. As a consequence the optimal value function can be obtained as the pointwise infimum of auxiliary value functions indexed by Lagrange multipliers. Finally, we illustrate our findings with a series of numerical examples.

math.OC↗