A new weak solution to an optimal stopping problem

Cong Qin; Xinfu Chen

doi:10.3934/dcdsb.2020128

Article Contents

2020, Volume 25, Issue 12: 4823-4837. Doi: 10.3934/dcdsb.2020128

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A new weak solution to an optimal stopping problem

Cong Qin^1, , and
Xinfu Chen^2,

1.
Center for Financial Engineering, Soochow University, Suzhou, Jiangsu 215006, China
2.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

^* Corresponding author: Cong Qin
^* Corresponding author: Cong Qin

Received: October 2019

Early access: April 2020

Published: December 2020

The first author received support from NSFC 11901416, NSF of Jiangsu BK20190812, and NSF for Universities in Jiangsu Province 19KJD100005

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Abstract

In this paper, we propose a new weak solution to an optimal stopping problem in finance and economics. The main advantage of this new definition is that we do not need the Dynamic Programming Principle, which is critical for both classical verification argument and modern viscosity approach. Additionally, the classical methods in differential equations, e.g. penalty method, can be used to derive some useful results.

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Mathematics Subject Classification: Primary: 35K86, 91G80; Secondary: 35Q93, 91G20.

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References

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