Geodesic
Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 457-467.

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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.
Classification : 41A35, 41A36, 47D06, 47E05, 47N10, 91B28, 91Gxx
Keywords: strongly continuous semigroups; differential operators; positive linear operators; Black-Scholes operator 
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     title = {Shape-preserving properties and asymptotic behaviour of the semigroup generated by the {Black-Scholes} operator},
     journal = {Czechoslovak Mathematical Journal},
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Attalienti, Antonio; Rasa, Ioan. Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 457-467. http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a10/