We study PDE of the form max{F(D2u,x)−f(x),H(Du)}=0 where F is uniformly elliptic and convex in its first argument, H is convex, f is a given function and u is the unknown. These equations are derived from dynamic programming in a wide class of stochastic singular control problems. In particular, examples of these equations arise in mathematical finance models involving transaction costs, in queuing theory, and spacecraft control problems. The main aspects of this work are to identify conditions under which solutions are uniquely defined and have Lipschitz continuous gradients.
1
University of Pennsylvania, Philadelphia, USA
2
Howard University, Washington, USA
Ryan Hynd; Henok Mawi. On Hamilton–Jacobi–Bellman equations with convex gradient constraints. Interfaces and free boundaries, Tome 18 (2016) no. 3, pp. 291-315. doi: 10.4171/ifb/365
@article{10_4171_ifb_365,
author = {Ryan Hynd and Henok Mawi},
title = {On {Hamilton{\textendash}Jacobi{\textendash}Bellman} equations with convex gradient constraints},
journal = {Interfaces and free boundaries},
pages = {291--315},
year = {2016},
volume = {18},
number = {3},
doi = {10.4171/ifb/365},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/365/}
}
TY - JOUR
AU - Ryan Hynd
AU - Henok Mawi
TI - On Hamilton–Jacobi–Bellman equations with convex gradient constraints
JO - Interfaces and free boundaries
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IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/365/
DO - 10.4171/ifb/365
ID - 10_4171_ifb_365
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