Approximation of the Snell envelope and american options prices in dimension one

Vlad Bally; Bruno Saussereau

ESAIM: Probability and Statistics (2002)

  • Volume: 6, page 1-19
  • ISSN: 1292-8100

Abstract

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We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.

How to cite

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Bally, Vlad, and Saussereau, Bruno. "Approximation of the Snell envelope and american options prices in dimension one." ESAIM: Probability and Statistics 6 (2002): 1-19. <http://eudml.org/doc/244689>.

@article{Bally2002,
abstract = {We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.},
author = {Bally, Vlad, Saussereau, Bruno},
journal = {ESAIM: Probability and Statistics},
keywords = {dynamic programming; snell envelope; optimal stopping; optimal stopping problem; Black-Scholes model; tree method},
language = {eng},
pages = {1-19},
publisher = {EDP-Sciences},
title = {Approximation of the Snell envelope and american options prices in dimension one},
url = {http://eudml.org/doc/244689},
volume = {6},
year = {2002},
}

TY - JOUR
AU - Bally, Vlad
AU - Saussereau, Bruno
TI - Approximation of the Snell envelope and american options prices in dimension one
JO - ESAIM: Probability and Statistics
PY - 2002
PB - EDP-Sciences
VL - 6
SP - 1
EP - 19
AB - We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.
LA - eng
KW - dynamic programming; snell envelope; optimal stopping; optimal stopping problem; Black-Scholes model; tree method
UR - http://eudml.org/doc/244689
ER -

References

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  6. [6] N. El Karoui, C. Kapoudjan, E. Pardoux, S. Peng and M.C. Quenez, Reflected Solutions of Backward Stochastic Differential Equations and related Obstacle Problems for PDE’s. Ann. Probab. 25 (1997) 702-737. Zbl0899.60047
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  9. [9] D. Lamberton, Brownian optimal stopping and random walks, Preprint 03/98. Université de Marne-la-Vallée (1998). Zbl1040.60032MR1885822
  10. [10] D. Lamberton and G. Pagès, Sur l’approximation des réduites. Ann. Inst. H. Poincaré Probab. Statist. 26 (1990) 331-335. Zbl0704.60042
  11. [11] D. Lamberton and C. Rogers, Optimal Stopping and Embedding, Preprint 17/99. Université de Marne-la-Vallée (1999). Zbl0981.60049
  12. [12] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. Springer Verlag, Berlin Heidelberg (1991). Zbl0731.60002MR1083357
  13. [13] A.W. Roberts and D.E. Varberg, Convex Functions. Academic Press, New York (1973). Zbl0271.26009MR442824
  14. [14] B. Saussereau, Sur une classe d’équations aux dérivées partielles. Ph.D. Thesis of the University of Le Mans, France (2000). 

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