First Order BSPDEs in higher dimension for optimal control problems

Abstract

The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations) suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman equations and allow to construct the value function for stochastic optimal control problems with unspecified dynamics where the underlying processes do not necessarily satisfy stochastic differential equations of a known kind with a given structure. The problems considered arise in financial modelling.

References in corpus (2)

• Random Periodic Solutions of SPDEs via Integral Equations and Wiener-Sobolev Compact Embedding
• A First-Order BSPDE for Swing Option Pricing: Classical Solutions