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On properties of solutions to Black–Scholes–Barenblatt equations
On properties of solutions to Black–Scholes–Barenblatt equations
- 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.
- Subjects :
- Comparison theorem
Strict comparison theorem
Algebra and Number Theory
Partial differential equation
Functional analysis
Applied Mathematics
lcsh:Mathematics
010102 general mathematics
Sigma
Strict sub-additivity
lcsh:QA1-939
01 natural sciences
010101 applied mathematics
Ordinary differential equation
Black–Scholes–Barenblatt equation
0101 mathematics
Analysis
Mathematical physics
Mathematics
Subjects
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