Determination of a source term in a partial differential equation arising in finance

Abstract

In this article, we discuss the Lipschitz stability for an inverse problem of determining the source term in option pricing. The main tool for establishing the result is the Carleman estimate.

Keywords:

• Carleman estimate
• Black–Scholes equation
• stability estimate

AMS Subject Classifications::

• 35K10
• 35Q80
• 35R30

Acknowledgement

The authors are grateful to the referee for raising several important questions and informing about the works 10, 11, 22.