Umut Cetin (London School of Economics): Dynamic Markov Bridges and Insider Trading

Motivated by the insider trading models of Kyle and Back, we present a theory of Markov bridges. We call them 'dynamic' since the terminal value is
not known in advance. In this talk I will describe how to construct a
diffusion which is a martingale and whose terminal value is defined by the
terminal value of another martingale diffusion observed continuously in
time. Our approach is based on nonlinear filtering theory and parabolic
pdes. If time permits I will also describe an application of our method for
the construction of a Brownian motion who is conditioned to hit 0 for the
first time at a deterministic function of the hitting time of another
Gaussian martingale and discuss its application to an insider trading model
for a defaultable derivative of European type.
The talk is based on joint works with L. Campi and A. Danilova.