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Backward stochastic equations and equilibrium pricing in incomplete financial markets 15:10 Fri 27 Nov 09 | Macbeth Lecture Theatre | Professor Ulrich Horst | Humboldt-University, Berlin
Abstract...The problem of equilibrium pricing in dynamically incomplete financial
markets is one of the oldest problems in mathematical economics. The
problem of equilibrium pricing is well understood for the benchmark case
of complete markets where all risk factors can be hedged using the
available assets. When markets are incomplete the situation is more
involved, and to date no unified approach to incomplete markets is
available. In this talk we review some recent results on equilibrium
pricing in incomplete markets in discrete time when the market
participants evaluate their risk exposures using dynamic risk measures.
For such market situations we establish existence and uniqueness of
equilibrium results and show that the problem of dynamic equilibrium
pricing can be reduced to a recursive sequence of static one-period
problems. When the flow of information is generated by independent random
walks the equilibrium dynamics can be described by a coupled system of
backward stochastic difference equations which renders our approach easily
amenable to numerical simulations. We also comment on some of the
mathematical challenges that currently prevent us from translating our
results from discrete to continuous time, including the lack of existence
and differentiability of solutions results for coupled systems of backward
stochastic differential equations with non Lipschitz continuous drivers.
The talk is based on joint work with Patrick Cheridito (Princeton
University), Michael Kupper (Humboldt University) and Traian A. Pirvu
(McMaster University)
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