Optimal Reflection of Diffusions and Barrier Options Pricing under Constraints

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. Keywords : Reflected diffusion, Skorokhod problem, viscosity solutions, barrier option, portfolio contraints. MSC Classification (2000): 93E20, 60G99, 49L25, 91B28.

• Type: Journal
• Year: 2008
• Where: SIAMCO
• Authors: Bruno Bouchard
• Keywords: Associated Value Function, Barrier Option, Bounded Variation, SIAMCO 2008