Given a Markovian Brownian martingale Z we build a process X which is a martingale in its own filtration such that its terminal value equals the terminal value of Z. We call X a dynamic bridge since the terminal value is not known in advance. More explicitly, X is adapted to the filtration generated by Z and an independent Brownian motion. Our construction is based on parabolic PDEs and filtering techniques. As an application we solve an equilibrium model with insider trading that can be viewed as a non-Gaussian generalization of the insider trading model of Back and Pedersen (1998).
Based on a joint work with L. Campi and A. Danilova.
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