We show the existence and the uniqueness of the solution for some multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type). Afterwards we consider optimal control problems where the state X is a solution of a controlled delay stochastic system as above. We establish the dynamic programming principle for the value function and finally we prove that the value function is a viscosity solution for a suitable Hamilton- Jacobi-Bellman type equation.
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