Dynamic Markov bridges motivated by models of insider trading

Luciano Campi, Umut Çetin and Albina Danilova

Stochastic Processes and their Applications, 2011, vol. 121, issue 3, 534-567

Abstract: Given a Markovian Brownian martingale Z, we build a process X which is a martingale in its own filtration and satisfies X1=Z1. We call X a dynamic bridge, because its terminal value Z1 is not known in advance. We compute its semimartingale decomposition explicitly under both its own filtration and the filtration jointly generated by X and Z. Our construction is heavily based on parabolic partial differential equations and filtering techniques. As an application, we explicitly solve an equilibrium model with insider trading that can be viewed as a non-Gaussian generalization of the model of Back and Pedersen (1998) [3], where the insider's additional information evolves over time.

Keywords: Markovian; bridges; Martingale; problem; Nonlinear; filtering; Parabolic; PDEs; Equilibrium; Insider; trading (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (22)

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