HJB equations with gradient constraint associated with controlled jump-diffusion processes
Analysis of PDEs
2019-03-26 v6
Abstract
In this paper, we guarantee the existence and uniqueness (in the almost everywhere sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient constraint and a partial integro-differential operator whose L\'evy measure has bounded variation. This type of equation arises in a singular control problem, where the state process is a multidimensional jump-diffusion with jumps of finite variation and infinite activity. We verify, by means of {\epsilon}-penalized controls, that the value function associated with this problem satisfies the aforementioned HJB equation.
Cite
@article{arxiv.1701.07291,
title = {HJB equations with gradient constraint associated with controlled jump-diffusion processes},
author = {Mark Kelbert and Harold A. Moreno-Franco},
journal= {arXiv preprint arXiv:1701.07291},
year = {2019}
}