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Asymptotic Equivalence Between Boundary Perturbations and Discrete Exit Times: Application to Simulation Schemes

  • E. Gobet
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)

Abstract

We present two problems that are apparently disconnected, and we show how they are actually related to each other. First, we investigate the sensitivity of the expectation of functionals of diffusion process stopped at the exit from a domain, as the boundary is perturbed. Second, we analyze the discrete monitoring bias when simulating stopped diffusions, emphasizing the role of overshoot asymptotics. Then, we derive a simple and accurate scheme for simulating stopped diffusions.

Keywords

Brownian Motion Exit Time Euler Scheme Barrier Option Boundary Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work has been partly done when the author was affiliated to Grenoble INP-Ensimag. The author is grateful to Grenoble Institute of Technology (BQR grant entitled Monte Carlo) and to the Chair Risques Financiers of the Fondation du Risque for their financial support.

The author also thanks the two referees for their valuable comments and suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Ecole PolytechniqueCMAPPalaiseau CedexFrance

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