Dynamic Markov bridges motivated by models of insider trading
Campi, Luciano; Cetin, Umut; Danilova, Albina (2011), Dynamic Markov bridges motivated by models of insider trading, Stochastic Processes and their Applications, 121, 3, p. 534-567. http://dx.doi.org/10.1016/j.spa.2010.11.004
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1202.2980
Journal nameStochastic Processes and their Applications
MetadataShow full item record
Abstract (EN)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 FX and the filtration FX,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) , where the insider’s additional information evolves over time.
Subjects / KeywordsMarkovian bridges; Martingale problem; Nonlinear filtering; Parabolic PDEs; Equilibrium; Insider trading
Showing items related by title and author.