Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications

Details Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications

2010-02-11

arxiv.org/abs/1002.2373v1

SIAM J. Control Optim. 45, 1 (2006) 74-106

Mathematics

Analysis of PDEs

Scientific paper

10.1137/S0363012904440897

In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we characterize the value function of a finite horizon stochastic control problem with unbounded controls as the unique viscosity solution of the corresponding dynamic programming equation.

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