Financial mathematics Seminar: Prof. Robert Elliott -- A General Theory of Finite State Backward Stochastic Difference Equations

Prof.  Robert Elliott (School of Mathematical Sciences, University of Adelaide and
Haskayne School of Business, University of Calgary) will speak on 

"A General Theory of Finite State Backward Stochastic Difference Equations" 

Abstract: 

By analogy with the theory of Backward Stochastic Differential Equations, we define
Backward Stochastic Difference Equations on spaces related to discrete time, finite
state processes.  This paper considers these processes as constructions in their own
right, not as approximations to the continuous case.  We establish the existence and
uniqueness of solutions under weaker assumptions than are needed in the continuous time
setting, and also establish a comparison theorem for these solutions.  The conditions of
this theorem are shown to approximate those required in the continuous time setting.  We
also explore the relationship between the driver F and the set of solutions; in
particular, we determine under what conditions the driver is uniquely determined by the
solution.  Applications to the theory of nonlinear expectations are explored, including
a representation result.