Anticipated backward stochastic variational inequalities with generalized reflection

Abstract

We study the existence and uniqueness of the strong solution for the following anticipated backward stochastic variational inequality with oblique subgradients, written under differential form: [Formula: see text] The generalized multivalued product term [Formula: see text] loses the maximal monotony property of its constituent subdifferential operator and, as a consequence, some specific techniques when approaching the above problem are mandatory. The univalued anticipated BSDE addressed in Peng and Yang [19] highlights the duality between these types of equations and stochastic differential delay equations, in order to solve a stochastic control problem. We also provide an example of an anticipated BSDE with time-dependent convex constraints, which can be reduced to our equation.