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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Convergence of reward functionals in a reselling model for a European option


Author: M. S. Pupashenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 135-148
MSC (2010): Primary 60J05, 60H10; Secondary 91Gxx, 91B70
Published electronically: February 2, 2012
MathSciNet review: 2768854
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Abstract: We consider an optimal reselling problem for a European option. A modification of the Cox-Ingersoll-Ross process is used to model the implied volatility. We construct a two-dimensional binomial-trinomial exponential approximation instead of the discrete approximation proposed by Pupashenko and Kukush (2008) in Theory Stoch. Process. 14(30), no. 3-4, 114-128. We use the results concerning the convergence of reward functionals for exponential price processes with independent log-increments obtained by Lundgren et al.(2008) in J. Numer. Appl. Math. 1(96), 90-113. We proved that there is no arbitrage strategy in the proposed discrete model.


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Additional Information

M. S. Pupashenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: myhailo.pupashenko@gmail.com

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00847-8
PII: S 0094-9000(2012)00847-8
Keywords: European option, American option, reselling problem, reward, convergence, optimal stopping time, discrete approximation, Markov process, binomial-trinomial approximation, Cox–Ingersoll–Ross process
Received by editor(s): April 22, 2010
Published electronically: February 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society