Optimal reflection of diffusions and barrier options pricing under constraints
Résumé
We introduce a new class of control problems in which the gain depends on the solution of a stochastic differential equation reflected at the boundary of a bounded domain, along directions which are controlled by a bounded variation process. We provide a PDE characterization of the associated value function. This study is motivated by applications in mathematical finance where such equations are related to the pricing of barrier options under portfolio constraints.
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