Parameter identification problem for a parabolic equation - application to the Black-Scholes option pricing model

Yury M. Korolev; Hideo Kubo; Anatoly G. Yagola

doi:10.1515/jip-2012-0043

Parameter identification problem for a parabolic equation - application to the Black-Scholes option pricing model

Yury M. Korolev, Hideo Kubo, Anatoly G. Yagola

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

Abstract

We consider an inverse problem of parameter identification for a parabolic equation. The underlying practical example is the reconstruction of the unknown drift in the extended Black-Scholes option pricing model. Using a priori information about the unknown solution (i.e. its Lipschitz constant), we provide a solution to this non-linear illposed problem, as well as an error estimate. Other types of a priori information may be used (for example, monotonicity and/or convexity of the unknown solution).

Original language	English
Pages (from-to)	327-337
Number of pages	11
Journal	Journal of Inverse and Ill-posed Problems
Volume	20
Issue number	3
Early online date	1 Sept 2012
DOIs	https://doi.org/10.1515/jip-2012-0043
Publication status	Published - 1 Sept 2012

Bibliographical note

Funding Information:
The first and the third authors thank the RFBR (grants 11-01-00040-a and 12-01-00524-a) for partial financial support.

Keywords

Black-scholes model
Error estimation
Ill-posed problems
Parameter identification

ASJC Scopus subject areas

Applied Mathematics

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10.1515/jip-2012-0043Licence: Unspecified

Cite this

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AU - Kubo, Hideo

AU - Yagola, Anatoly G.

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N2 - We consider an inverse problem of parameter identification for a parabolic equation. The underlying practical example is the reconstruction of the unknown drift in the extended Black-Scholes option pricing model. Using a priori information about the unknown solution (i.e. its Lipschitz constant), we provide a solution to this non-linear illposed problem, as well as an error estimate. Other types of a priori information may be used (for example, monotonicity and/or convexity of the unknown solution).

AB - We consider an inverse problem of parameter identification for a parabolic equation. The underlying practical example is the reconstruction of the unknown drift in the extended Black-Scholes option pricing model. Using a priori information about the unknown solution (i.e. its Lipschitz constant), we provide a solution to this non-linear illposed problem, as well as an error estimate. Other types of a priori information may be used (for example, monotonicity and/or convexity of the unknown solution).

KW - Black-scholes model

KW - Error estimation

KW - Ill-posed problems

KW - Parameter identification

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ER -

Parameter identification problem for a parabolic equation - application to the Black-Scholes option pricing model

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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