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

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.
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Francesca da Lio, Olivier Ley. Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2006, 45 (1), pp.74-106. ⟨10.1137/S0363012904440897⟩. ⟨hal-00455993⟩

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