The paper studies the first order backward stochastic partial differential equations suggested earlier for one-dimensional state space. Some examples of similar equations are obtained for a multidimensional state space . These equations represent analogs of Hamilton-Jacobi-Bellman equations for the value functions of optimal control problems in non-Markovian setting arising in financial modelling.
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.
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first order backward stochastic partial differential equations
First Order BSPDEs (Backward Stochastic Partial Differential Equations)
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one-dimensional state space. Some examples of similar equations are obtained for a multidimensional state space
a case of multidimensional state domain with a boundary
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for the value functions of
and allow to construct the value function for stochastic
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in non-Markovian setting arising
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