Hamilton-Jacobi-Bellman equations with gradient constraint and an integro-differential operator

Mark Kelbert, Harold A. Moreno-Franco

Published 2017-01-25Version 1

Existence, regularity and uniqueness of the solution to a Hamilton-Jacobi-Bellman (HJB) equation was studied recently in [H. A. Moreno-Franco, Appl. Math. Opt. 2016], when the L\'evy measure associated with the integral part of the elliptic integro-differential operator, is finite. Here we extend the results obtained in this paper, in the case that the coefficients of the differential part of the elliptic integro-differential operator are not constants, and the L\'evy measure associated with this operator has bounded variation. The HJB equation studied in this work arises in singular stochastic control problems where the state process is a jump-diffusion.