Reflected BSDEs in Nonconvex Domains



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Sergey Nadtochiy, Associate Professor, Department of Applied Math, Illinois Institute of Technology



Backward stochastic differential equations (BSDEs) are probabilistic
analogues of semi-linear partial differential equations (PDEs). In particular, BSDEs
are used to describe the solutions of stochastic control problems and equilibria in
stochastic dynamic games. If a control problem includes impulse-type control (i.e.,
an option to move the state process instantaneously or to stop the game), then,
the associated PDE obtains a free-boundary feature. Similarly, the associated
BSDE becomes reflected: i.e. its solution lives inside a given domain and is
reflected at the boundary of this domain. The theory of reflected BSDEs in
dimension one (i.e., when the reflected process is one-dimensional) is well
developed in a very high generality. However, until now, the well-posedness of
multidimensional reflected BSDEs (which appear in some control problems and in
most games) has only been established in the case of a convex reflection domain.
I will present the first well-posedness result for the reflected BSDEs in non-convex
domains, an example of which appears in the buyer-seller games for market
microstructure. This is a joint work with J.-F. Chassagneux and A. Richou.

(1 hour talk, plus 15 minute Q&A)


Mathematical Finance, Stochastic Analysis, and Machine Learning 


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