Tug-of-war, market manipulation and option pricing
2014 (English)In: Mathematical Finance, ISSN 0960-1627, E-ISSN 1467-9965Article in journal (Refereed) Published
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
infinity Laplace;nonlinear parabolic partial differential equation;option pricing;stochastic differential game;tug-of-war
IdentifiersURN: urn:nbn:se:uu:diva-214209DOI: 10.1111/mafi.12090OAI: oai:DiVA.org:uu-214209DiVA: diva2:684421