Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

Title:

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

Creator:

Attalienti, Antonio and Rasa, Ioan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:18293ea6-eb23-4b7a-8103-8e33c5417d1d
uuid:18293ea6-eb23-4b7a-8103-8e33c5417d1d

Subject:

strongly continuous semigroups, differential operators, positive linear operators, and Black-Scholes operator

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the solutions of classical problems in option pricing theory in Mathematical Finance.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

457-467

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:2

Harvested from:

CDK

Metadata only:

false