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Optimal reflection of diffusions and barrier options pricing under constraints

Abstract : 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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Contributor : Bruno Bouchard <>
Submitted on : Thursday, September 21, 2006 - 5:39:20 PM
Last modification on : Thursday, December 10, 2020 - 11:08:42 AM
Long-term archiving on: : Friday, May 13, 2011 - 11:57:17 PM

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Bruno Bouchard. Optimal reflection of diffusions and barrier options pricing under constraints. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2008, 47 (4), pp.1785-1813. ⟨hal-00097537⟩

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