Uniqueness for Viscosity Solutions of Nonstationary Hamilton–Jacobi–Bellman Equations under Some a Priori Conditions (with Applications)

This paper extends the uniqueness results for viscosity solutions of nonstationary Hamilton–Jacobi–Bellman equations. The conditions for uniqueness which are obtained can involve a trade-off between the growth of the solution and the growth of the Hamiltonian. In particular, the result is valid for solutions which grow quadratically in the space variable and are associated with Hamiltonians which also grow quadratically. This particular class arises in the robust control limit of risk-sensitive stochastic control problems.