Dynamic Markov bridges motivated by models of insider trading

作者：Campi Luciano; Cetin Umut^*; Danilova Albina

来源：Stochastic Processes and Their Applications, 2011, 121(3): 534-567.

DOI：10.1016/j.spa.2010.11.004

• Markovian bridges
• Martingale problem
• Nonlinear filtering
• Parabolic PDEs
• Equilibrium
• Insider trading

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 its semimartingale decomposition explicitly under both its own filtration F-X and the filtration F-X.Z 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.

• 出版日期2011-3