Dynamic Markov bridges motivated by models of insider trading

Luciano Campi (1, 2) , Umut Cetin (3) , Albina Danilova (4)

1 FiME Lab - Laboratoire de Finance des Marchés d'Energie
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Department of Statistics, LSE
4 LSE - Department Mathematics [London]

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 (1998), where insider's additional information evolves over time.

Domaines: Probabilités [math.PR]

Luciano Campi, Umut Cetin, Albina Danilova. Dynamic Markov bridges motivated by models of insider trading. Stochastic Processes and their Applications, 2011, 121 (3), pp.534-567. ⟨hal-00533936⟩