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Tug-of-war, market manipulation and option pricing
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
University of Jyväskylä, Jyväskylä, Finland.
2014 (English)In: Mathematical Finance, ISSN 0960-1627, E-ISSN 1467-9965Article in journal (Refereed) Published
Abstract [en]

We develop an option pricing model based on a tug-of-war game involving the the issuer and holder of the option. This two-player zero-sum stochastic differential game is formulated in a multi-dimensional financial market and the agents try, respectively, to manipulate/control the drift and the volatility of the asset processes in order to minimize and maximize the expected discounted pay-off defined at the terminal date $T$. We prove that the game has a value  and that the value function is the unique viscosity solution to a terminal value problem for a partial differential equation involving the  non-linear and completely degenerate  parabolic infinity Laplace operator.

Place, publisher, year, edition, pages
Keyword [en]
infinity Laplace;nonlinear parabolic partial differential equation;option pricing;stochastic differential game;tug-of-war
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URN: urn:nbn:se:uu:diva-214209DOI: 10.1111/mafi.12090OAI: oai:DiVA.org:uu-214209DiVA: diva2:684421
Available from: 2014-01-08 Created: 2014-01-08 Last updated: 2016-07-20Bibliographically approved

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Nyström, Kaj
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