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Research Article | Open Access

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

School of Economics and Management, Chongqing Normal University, Chongqing 401331, China
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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 inequalitiesAmerican put optiondouble-phase degenerate parabolic operator with variable exponentsexistenceuniqueness

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Electronic Research Archive
Volume 34 Issue 2,
February 2026
Pages 1063-1078
DOI: 10.3934/era.2026049

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Cite this article:
Zhao Q. 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. Electronic Research Archive, 2026, 34(2): 1063-1078. https://doi.org/10.3934/era.2026049

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Received: 09 September 2025
Revised: 31 December 2025
Accepted: 19 January 2026
Published: 30 January 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)