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Optimal reflection of diffusions and barrier options pricing under constraints

Bouchard, Bruno (2008), Optimal reflection of diffusions and barrier options pricing under constraints, SIAM Journal on Control and Optimization, 47, 4, p. 1785–1813. http://dx.doi.org/10.1137/070697161

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Type
Article accepté pour publication ou publié
Date
2008
Journal name
SIAM Journal on Control and Optimization
Volume
47
Number
4
Publisher
Society for Industrial and Applied Mathematics
Pages
1785–1813
Publication identifier
http://dx.doi.org/10.1137/070697161
Metadata
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Author(s)
Bouchard, Bruno
Abstract (EN)
We introduce a new class of control problems in which the gain depends on the solu- tion of a stochastic differential equation (SDE) 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.
Subjects / Keywords
Viscosity solutions; Reflected diffusion; Mathematical Finance
JEL
G10 - General

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