Optimal withdrawals in a general diffusion model with control rates subject to a state-dependent upper bound
Abstract
We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the first-passage time below level zero. In this work, we are considering absolutely continuous control strategies in a general diffusion model. Our main contribution is a solution to the control problem under study, which is achieved by using a probabilistic guess-and-verify approach. We prove that the optimal strategy belongs to the family of bang-bang strategies, i.e. strategies in which, above an optimal barrier level, we withdraw at the highest-allowed rate, while no withdrawals are made below this barrier. Some nontrivial examples are studied numerically.
Cite
@article{arxiv.2406.12067,
title = {Optimal withdrawals in a general diffusion model with control rates subject to a state-dependent upper bound},
author = {Hélène Guérin and Dante Mata and Jean-François Renaud and Alexandre Roch},
journal= {arXiv preprint arXiv:2406.12067},
year = {2024}
}