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

2017/01/25 by Kelbert, Mark, Moreno-Franco, Harold A.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.07291

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.

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