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Sensitivity analysis for reflected diffusions in convex polyhedral domains

Banff International Research Station for Mathematical Innovation and Discovery

Differentiability of flows and sensitivity analysis are classical topics in dynamical systems. However, the analysis of these properties for constrained processes, which arise in a variety of applications, is challenging due to the discontinuities in the dynamics at the boundary of the domain, and is further complicated when the boundary is non-smooth. We establish pathwise differentiability of a large class of obliquely reflected diffusions in convex polyhedron domains and characterize the derivative process as a (degenerate) Markov process that satisfies a stochastic differential equation with time-varying domain and directions of reflection. We also provide conditions under which this Markov process has a unique invariant distribution, and discuss its relevance for calculating sensitivities of performance measures in the so-called Atlas Model in mathematical finance. (This is based on joint work with David Lipshutz.)

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes

video/mp4

Author affiliation: Brown University

2017-06-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/62027

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/