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arXiv · 1410.1664

Tug-of-war, market manipulation and option pricing

Kaj Nyström·Mikko Parviainen
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Abstract

We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. 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 parabolic partial differential equation involving the non-linear and completely degenerate infinity Laplace operator.

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Kaj Nyström, Mikko Parviainen. 2014-10-07. Tug-of-war, market manipulation and option pricing. https://arxiv.org/abs/1410.1664

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