Existence and uniqueness of solutions to variational inequalities involving a double-phase degenerate parabolic operator with variable exponents arising from American put option valuation analysis

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Abstract

This paper analyzes a class of variational inequalities involving a double-phase degenerate parabolic operator with variable exponents, which arises in the valuation of American put options. By establishing energy estimates for the associated penalty problem and applying a limiting argument, the existence of a weak solution is obtained. The uniqueness of the weak solution is also discussed.

Keywords

variational inequalities / American put option / double-phase degenerate parabolic operator with variable exponents / existence / uniqueness

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