2014/10/07 by Nyström, Kaj, Parviainen, Mikko
#35K59 #49L25 #60H15 #91A15 #91A23 #91G80 #Analysis of PDEs (math.AP) #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Pricing of Securities (q-fin.PR) #Probability (math.PR)
paper · doi:10.48550/arxiv.1410.1664
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.