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On properties of solutions to Black–Scholes–Barenblatt equations

On properties of solutions to Black–Scholes–Barenblatt equations

Authors :
Weicheng Xu
Yiqing Lin
Xinpeng Li
Source :
Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-9 (2019)
Publication Year :
2019
Publisher :
SpringerOpen, 2019.

Abstract

This paper is concerned with the Black–Scholes–Barenblatt equation $\partial _{t}u+r(x\partial _{x}u-u)+G(x^{2}\partial _{xx}u)=0$ , where $G(\alpha )=\frac{1}{2}(\overline{\sigma}^{2}-\underline{\sigma}^{2})|\alpha |+\frac{1}{2}(\overline{\sigma}^{2}+\underline{\sigma}^{2})\alpha $ , $\alpha \in \mathbb{R}$ . This equation is usually used for derivative pricing in the financial market with volatility uncertainty. We discuss a strict comparison theorem for Black–Scholes–Barenblatt equations, and study strict sub-additivity of their solutions with respect to terminal conditions.

Details

Language :
English
ISSN :
16871847
Volume :
2019
Issue :
1
Database :
OpenAIRE
Journal :
Advances in Difference Equations
Accession number :
edsair.doi.dedup.....61dc9d81e846c55fe3264792e4675fde
Full Text :
https://doi.org/10.1186/s13662-019-2135-z