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

Authors:
Francesca Da Lio;Olivier Ley
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2006

Citing 0
Cited 3

Brief paper: Solution to a class of stochastic LQ problems with bounded control

Automatica (Journal of IFAC)
Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton-Jacobi Equations with Superquadratic Growth in the Gradient

SIAM Journal on Control and Optimization
Convergence by Viscosity Methods in Multiscale Financial Models with Stochastic Volatility

SIAM Journal on Financial Mathematics

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Abstract

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.