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arXiv · 1701.07291

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

Mark Kelbert·Harold A. Moreno-Franco
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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.

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Mark Kelbert, Harold A. Moreno-Franco. 2017-01-25. HJB equations with gradient constraint associated with controlled jump-diffusion processes. https://arxiv.org/abs/1701.07291

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