  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.
