On non-uniqueness of solutions to degenerate parabolic equations in the context of option pricing in the Heston model

Abstract

It is known that the price of call options in the Heston model is determined in a non-unique way. In this paper, this problem is analyzed from the point of view of the existing mathematical theory of uniqueness classes for degenerate parabolic equations. For the special case of degeneracy, a new example is constructed demonstrating the accuracy of the uniqueness theorem for a solution in the class of functions with sublinear growth at infinity.

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