Study of weak solutions of variational inequality systems with degenerate parabolic operators and quasilinear terms arising Americian option pricing problems

Jia Li; Changchun Bi; Jia Li; Changchun Bi

doi:10.3934/math.20221083

AIMS Mathematics

2022, Volume 7, Issue 11: 19758-19769. doi: 10.3934/math.20221083

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Research article

Study of weak solutions of variational inequality systems with degenerate parabolic operators and quasilinear terms arising Americian option pricing problems

Jia Li ,
Changchun Bi ^,

School of Management, Shenyang Urban Construction University, Shenyang, Liaoning, 110167, China

Received: 28 June 2022 Revised: 18 August 2022 Accepted: 19 August 2022 Published: 06 September 2022
MSC : 35K99, 97M30

In this paper, we study variational inequality systems with quasilinear degenerate parabolic operators in a bounded domain. As a series of penalty problems, the existence of the solutions in the weak sense is proved by a limit process. The uniqueness of the solution is also proved.
- parabolic variational inequality,
- weak solution,
- penalty problem,
- existence,
- uniqueness,
- Americian option pricing
Citation: Jia Li, Changchun Bi. Study of weak solutions of variational inequality systems with degenerate parabolic operators and quasilinear terms arising Americian option pricing problems[J]. AIMS Mathematics, 2022, 7(11): 19758-19769. doi: 10.3934/math.20221083

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Abstract

In this paper, we study variational inequality systems with quasilinear degenerate parabolic operators in a bounded domain. As a series of penalty problems, the existence of the solutions in the weak sense is proved by a limit process. The uniqueness of the solution is also proved.

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