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Game theoretic analysis of incomplete markets : emergence of probabilities, nonlinear and fractional Black–Scholes equations
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Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2013) Game theoretic analysis of incomplete markets : emergence of probabilities, nonlinear and fractional Black–Scholes equations. Risk and Decision Analysis, Volume 4 (Number 3). pp. 131-161. doi:10.3233/RDA-2011-0062 ISSN 1569-7371.
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Official URL: http://iospress.metapress.com/content/97t125060235...
Abstract
Expanding the ideas of the author's paper “Nonexpansive maps and option pricing theory” [Kibernetica 34(6) (1998), 713–724] we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral probabilities emerge automatically from the robust control evaluation. This approach seems to be especially appealing for incomplete markets encompassing extensive, so to say untamed, randomness, when the coexistence of infinite number of risk neutral measures precludes one from unified pricing of derivative securities. Our method is robust enough to be able to accommodate various markets rules and settings including path dependent payoffs, American options and transaction costs. On the other hand, it leads to rather simple numerical algorithms. Continuous time limit is described by nonlinear and/or fractional Black–Scholes type equations.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Risk and Decision Analysis | ||||
Publisher: | IOS Press | ||||
ISSN: | 1569-7371 | ||||
Official Date: | 12 August 2013 | ||||
Dates: |
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Volume: | Volume 4 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 131-161 | ||||
DOI: | 10.3233/RDA-2011-0062 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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