| Abstract: |
| In this talk, we investigate a stochastic optimal control problem in which the performance criterion is described by a reflected backward stochastic differential equation (RBSDE) subject to a lower obstacle. The reflection mechanism introduces intrinsic nonsmoothness, which prevents the direct application of standard variational techniques.
To address this difficulty, we employ a penalization method, approximating the RBSDE by a sequence of classical BSDEs augmented with penalization terms. Combining spike variation arguments with duality techniques, we establish a Pontryagin-type maximum principle for the penalized systems and subsequently pass to the limit.
In the limiting framework, we derive a novel adjoint equation that involves a singular measure concentrated on the contact set where the reflection constraint is active. This measure can be interpreted as a stochastic counterpart of a Lagrange multiplier, yielding a rigorous Hamiltonian formulation of the maximum principle under state inequality constraints.
In this talk, we also illustrate the theoretical results with a representative example. |
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