# Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 1, page 112-128
- ISSN: 1292-8119

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topHynd, Ryan. "Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 112-128. <http://eudml.org/doc/272884>.

@article{Hynd2013,

abstract = {We study the partial differential equation max\{Lu − f, H(Du)\} = 0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Hölder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous.},

author = {Hynd, Ryan},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {HJB equation; gradient constraint; free boundary problem; singular control; penalty method; viscosity solutions; Hamilton-Jacobi-Bellman equation},

language = {eng},

number = {1},

pages = {112-128},

publisher = {EDP-Sciences},

title = {Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control},

url = {http://eudml.org/doc/272884},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Hynd, Ryan

TI - Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 1

SP - 112

EP - 128

AB - We study the partial differential equation max{Lu − f, H(Du)} = 0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Hölder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous.

LA - eng

KW - HJB equation; gradient constraint; free boundary problem; singular control; penalty method; viscosity solutions; Hamilton-Jacobi-Bellman equation

UR - http://eudml.org/doc/272884

ER -

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