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Regular version of the site

Article

HJB equations with gradient constraint associated with controlled jump-di usion processes

SIAM Journal on Control and Optimization. 2019. Vol. 57. No. 3. P. 2185-2213.
Kelbert M., Moreno-Franco H.

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-di erential operator whose Levy measure has bounded
variation. This type of equation arises in a singular control problem, where the state
process is a multidimensional jump-di usion with jumps of finite variation and infinite
activity. We verify, by means of "-penalized controls, that the value function associated
with this problem satis es the aforementioned HJB equation.