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.
Mots clés : dynamic programming, snell envelope, optimal stopping
@article{PS_2002__6__1_0, author = {Bally, Vlad and Saussereau, Bruno}, title = {Approximation of the {Snell} envelope and american options prices in dimension one}, journal = {ESAIM: Probability and Statistics}, pages = {1--19}, publisher = {EDP-Sciences}, volume = {6}, year = {2002}, doi = {10.1051/ps:2002001}, mrnumber = {1888135}, zbl = {0998.60037}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps:2002001/} }
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 SP - 1 EP - 19 VL - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2002001/ DO - 10.1051/ps:2002001 LA - en ID - PS_2002__6__1_0 ER -
%0 Journal Article %A Bally, Vlad %A Saussereau, Bruno %T Approximation of the Snell envelope and american options prices in dimension one %J ESAIM: Probability and Statistics %D 2002 %P 1-19 %V 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2002001/ %R 10.1051/ps:2002001 %G en %F PS_2002__6__1_0
Bally, Vlad; Saussereau, Bruno. Approximation of the Snell envelope and american options prices in dimension one. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 1-19. doi : 10.1051/ps:2002001. http://archive.numdam.org/articles/10.1051/ps:2002001/
[1] Error estimates and free-boundary convergence for a finite-difference discretization of a parabolic variational inequality. RAIRO Anal. Numér./Numer. Anal. 11 (1977) 315-340. | Numdam | MR | Zbl
and ,[2] Reflected BSDE's, PDE's and Variational Inequalities. J. Theoret. Probab. (submitted).
, and ,[3] Applications of the Variational Inequalities in Stochastic Control. North Holland (1982). | MR | Zbl
and ,[4] Handbook of Brownian Motion Facts and Formulae. Birkhauser (1996). | MR | Zbl
and ,[5] American option valuation: New bounds, approximations, and a comparison of existing methods. Rev. Financial Stud. 9 (1995) 1211-1250.
and ,[6] Reflected Solutions of Backward Stochastic Differential Equations and related Obstacle Problems for PDE's. Ann. Probab. 25 (1997) 702-737. | Zbl
, , , and ,[7] An Introduction to Probability Theory and its Applications, Vol. II. John Wiley and Sons (1966). | MR | Zbl
,[8] Error Estimates for the Binomial Approximation of American Put Options. Ann. Appl. Probab. 8 (1998) 206-233. | MR | Zbl
,[9] Brownian optimal stopping and random walks, Preprint 03/98. Université de Marne-la-Vallée (1998). | MR | Zbl
,[10] Sur l'approximation des réduites. Ann. Inst. H. Poincaré Probab. Statist. 26 (1990) 331-335. | Numdam | Zbl
and ,[11] Optimal Stopping and Embedding, Preprint 17/99. Université de Marne-la-Vallée (1999). | Zbl
and ,[12] Continuous Martingales and Brownian Motion. Springer Verlag, Berlin Heidelberg (1991). | MR | Zbl
and ,[13] Convex Functions. Academic Press, New York (1973). | MR | Zbl
and ,[14] Sur une classe d'équations aux dérivées partielles. Ph.D. Thesis of the University of Le Mans, France (2000).
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