Dynamic Markov bridges motivated by models of insider trading

Luciano Campi, Umut \c{C}etin and Albina Danilova

Papers from arXiv.org

Abstract: Given a Markovian Brownian martingale $Z$, we build a process $X$ which is a martingale in its own filtration and satisfies $X_1 = Z_1$. We call $X$ a dynamic bridge, because its terminal value $Z_1$ is not known in advance. We compute explicitly its semimartingale decomposition under both its own filtration $\cF^X$ and the filtration $\cF^{X,Z}$ jointly generated by $X$ and $Z$. Our construction is heavily based on parabolic PDE's 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 Back and Pedersen's \cite{BP}, where insider's additional information evolves over time.

Date: 2012-02
New Economics Papers: this item is included in nep-mst
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Published in Stochastic processes and their applications, 2011, 121 (3). pp. 534-567

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