Lévy random bridges and the modelling of financial information (Q544493)

The paper introduces a wide class of information processes as a basis for the generation of market filtrations. More precisely, Lévy bridges are introduced as stochastic processes defined over a finite time horizon; they are Lévy processes whose terminal values are known from the outset. A proof of the Markov property for Lévy bridges is provided. Then, Lévy random bridges are defined as processes with finite time horizon whose bridge laws are the bridge laws of Lévy processes. Such processes are useful for asset pricing in the information-based framework. Their basic properties are studied. Using Bayesian methods, the dynamics of the price of a cash flow is derived and European call options are priced on the cash flow price.