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Existence and uniqueness of martingale solutions to option pricing equations with noise. (English) Zbl 1464.35347

Summary: We introduce a new option pricing equation with noise in a frictional financial market, which is fully different from the classical option pricing equation, and arrive at the existence of martingale solutions of this option pricing equation regardless of incompressibility. Furthermore, we also discuss the uniqueness of martingale solutions.

MSC:

35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
35Q30 Navier-Stokes equations
91B24 Microeconomic theory (price theory and economic markets)
91G20 Derivative securities (option pricing, hedging, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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