An essay on the general theory of stochastic processes

Abstract

This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school and which are usually written in French. The material presented in the last three chapters is less standard and takes into account some recent developments.

Published at http://dx.doi.org/10.1214/154957806000000104 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• How badly are the Burholder-Davis-Gundy inequalities affected by arbitrary random times?

Cited by in corpus (25)

• On arbitrages arising from honest times
• Local solution method for the problem of enlargement of filtration
• Default times, non arbitrage conditions and change of probability measures
• From Black-Scholes and Dupire formulae to last passage times of local martingales. Part A : The infinite time horizon
• On honest times in financial modeling
• Exercices sur les temps locaux de semi-martingales continues et les excursions browniennes
• Optimal market making under partial information with general intensities
• Reflected BSDEs when the obstacle is not right-continuous and optimal stopping
• Progressive Enlargements of Filtrations with Pseudo-Honest Times and their Applications in Financial Mathematics
• A generalization of Doob's maximal identity
• Reflected BSDEs with two completely separated barriers and regulated trajectories in general filtration
• Quantum $S{L}_2$, Infinite curvature and Pitman's 2M-X theorem
• Hazard processes and martingale hazard processes
• Skorohod equation and BSDE's with two reflecting barriers
• Shadow prices for continuous processes
• Utility Maximization and Indifference Value under Risk and Information Constraints for a Market with a Change Point
• Some No-Arbitrage Rules For Converging Asset Prices under Short-Sales Constraints
• Optimal market making under partial information and numerical methods for impulse control games with applications
• The Infinite Horizon Investment-Consumption Problem for Epstein-Zin Stochastic Differential Utility
• Existence and uniqueness for reflected BSDE with multivariate point process and right upper-semi-continuous obstacle
• Risk-indifference Pricing of American-style Contingent Claims
• Reflected and Doubly RBSDEs with Irregular Obstacles and a Large Set of Stopping Strategies
• Backwards semi-martingales into Burgers' turtulence
• Doubly Reflected BSDEs in the predictable setting
• Independence times for iid sequences, random walks and Lévy processes