HJB equations with gradient constraint associated with controlled jump-diffusion processes

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 Lévy 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 ε-penalized controls, that the value function associated with this problem satisfies the aforementioned HJB equation.

References in corpus (2)

• On the optimal dividend problem for a spectrally negative Lévy process
• Solution to HJB equations with an elliptic integro-differential operator and gradient constraint