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Functional convergence of Snell envelopes: Applications to American options approximations

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  • Maurizio Pratelli

    (Dipartimento di Matematica, UniversitÁ di Pisa, Via Buonarroti 2, I-56100 Pisa, Italy Manuscript)

  • Sabrina Mulinacci

    (Istituto di Econometria e Matematica per le Decisioni Economiche, UniversitÁ Cattolica del S. Cuore, Via Necchi 9, I-20131 Milano, Italy)

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    Abstract

    The main result of the paper is a stability theorem for the Snell envelope under convergence in distribution of the underlying processes: more precisely, we prove that if a sequence $(X^n)$ of stochastic processes converges in distribution for the Skorokhod topology to a process $X$ and satisfies some additional hypotheses, the sequence of Snell envelopes converges in distribution for the Meyer-Zheng topology to the Snell envelope of $X$ (a brief account of this rather neglected topology is given in the appendix). When the Snell envelope of the limit process is continuous, the convergence is in fact in the Skorokhod sense. This result is illustrated by several examples of approximations of the American options prices; we give moreover a kind of robustness of the optimal hedging portfolio for the American put in the Black and Scholes model.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 2 (1998)
    Issue (Month): 3 ()
    Pages: 311-327

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    Handle: RePEc:spr:finsto:v:2:y:1998:i:3:p:311-327

    Note: received: January 1996; final version received: July 1997
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: American options; Snell envelopes; convergence in distribution; optimal stopping times;

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    Cited by:
    1. Dietmar P.J. Leisen, 1997. "The Random-Time Binomial Model," Finance, EconWPA 9711005, EconWPA, revised 29 Nov 1998.
    2. Yan Dolinsky, 2009. "Applications of weak convergence for hedging of game options," Papers 0908.3661, arXiv.org, revised Nov 2010.

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