×

zbMATH — the first resource for mathematics

Sowrirajan, R.; Balachandran, K.
Determination of a source term in a partial differential equation arising in finance. (English) Zbl 1170.35328
Appl. Anal. 88, No. 1, 131-140 (2009).
Summary: 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.

Cited in 1 Document
MSC:
35B35 Stability in context of PDEs
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
35R30 Inverse problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
91G80 Financial applications of other theories
Keywords:
Carleman estimate; Black-Scholes equation; stability estimate
PDF BibTeX XML Cite
\textit{R. Sowrirajan} and \textit{K. Balachandran}, Appl. Anal. 88, No. 1, 131--140 (2009; Zbl 1170.35328)
Full Text: DOI
References:
[1] DOI: 10.1086/260062 · Zbl 1092.91524 · doi:10.1086/260062
[2] DOI: 10.1016/j.jmaa.2004.08.067 · Zbl 1114.91044 · doi:10.1016/j.jmaa.2004.08.067
[3] DOI: 10.1088/0266-5611/13/5/001 · Zbl 0894.90014 · doi:10.1088/0266-5611/13/5/001
[4] DOI: 10.1088/0266-5611/15/3/201 · Zbl 0938.35190 · doi:10.1088/0266-5611/15/3/201
[5] DOI: 10.1016/j.aml.2002.12.016 · Zbl 1068.35005 · doi:10.1016/j.aml.2002.12.016
[6] DOI: 10.1137/S0036142999355921 · Zbl 0990.35013 · doi:10.1137/S0036142999355921
[7] DOI: 10.1088/0266-5611/14/5/009 · Zbl 0992.35110 · doi:10.1088/0266-5611/14/5/009
[8] Adams RA, Sobolev Spaces, 2. ed. (2003)
[9] Hormander L, The Analysis of Linear Partial Differential Operators (1983)
[10] DOI: 10.1080/00036819308840186 · Zbl 0795.35134 · doi:10.1080/00036819308840186
[11] DOI: 10.1088/0266-5611/7/4/007 · Zbl 0744.35065 · doi:10.1088/0266-5611/7/4/007
[12] Fursikov AV, Lecture Notes Series, Vol. 34, in: Controllability of Evolution Equations (1996) · Zbl 0862.49004
[13] DOI: 10.1002/cpa.10072 · Zbl 1121.93306 · doi:10.1002/cpa.10072
[14] DOI: 10.1016/j.camwa.2006.11.007 · Zbl 1119.93020 · doi:10.1016/j.camwa.2006.11.007
[15] DOI: 10.1515/156939403766493519 · Zbl 1056.35148 · doi:10.1515/156939403766493519
[16] DOI: 10.1088/0266-5611/21/1/017 · Zbl 1086.35132 · doi:10.1088/0266-5611/21/1/017
[17] DOI: 10.1088/0266-5611/20/4/002 · Zbl 1061.35168 · doi:10.1088/0266-5611/20/4/002
[18] DOI: 10.1080/00036810500474788 · Zbl 1274.35413 · doi:10.1080/00036810500474788
[19] Bukhgeim AL, Soviet Math. Dokl 24 pp 244– (1981)
[20] DOI: 10.1088/0266-5611/8/4/009 · Zbl 0755.35151 · doi:10.1088/0266-5611/8/4/009
[21] Isakov V, Inverse Problems for Partial Differential Equations (1998)
[22] Klibanov MV, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (2004) · doi:10.1515/9783110915549
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.