Modulus of continuity of Nemytskii operators with application to the problem of option pricing : Journal of Inverse and Ill-posed Problems Jump to ContentJump to Main Navigation
Show Summary Details

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712

Mathematical Citation Quotient (MCQ) 2015: 0.43

249,00 € / $374.00 / £187.00*

Online
ISSN
1569-3945
See all formats and pricing
Select Volume and Issue
Loading journal volume and issue information...

30,00 € / $42.00 / £23.00

Get Access to Full Text

Modulus of continuity of Nemytskii operators with application to the problem of option pricing

R. Krämer1 / P. Mathé2

1 Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany. Email:

2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 5, Pages 435–461, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.024, September 2008

Publication History

Received:
2008-02-11
Revised:
2008-03-18
Published Online:
2008-09-12

Abstract

We introduce and analyze moduli of continuity for specific classes of Nemytskii operators on spaces of continuous functions, which are given by kernels, strictly monotone in their second argument. Such operators occur as non-linear (outer) mappings for certain problems of option pricing within the Black–Scholes model for time-dependent volatility. This nonlinear mapping can be seen to be continuous, however its convergence properties are poor. Our general results allow to bound the related moduli of continuity, both for the forward and backward non-linear mappings. In particular we explain the observed ill-conditioning of the nonlinear backward problem. The analysis uses some abstract local analysis of index functions, which may be of independent interest.

Key words.: Nemytskii operator; modulus of continuity; Black–Scholes model; local analysis

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Dang Duc Trong, Dinh Ngoc Thanh, and Nguyen Nhu Lan
Vietnam Journal of Mathematics, 2015
[2]
Jin Cheng, Bernd Hofmann, and Shuai Lu
Journal of Computational and Applied Mathematics, 2014, Volume 265, Page 110
[3]
Dang Duc Trong, Dinh Ngoc Thanh, Nguyen Nhu Lan, and Pham Hoang Uyen
Applicable Analysis, 2014, Volume 93, Number 4, Page 859
[4]
B. Hofmann, R. Krämer, and M. Richter
International Journal of Computer Mathematics, 2009, Volume 86, Number 6, Page 992

Comments (0)

Please log in or register to comment.