An interesting family of Black-Scholes perpetuities

Bernard Roynette (1, 2) , Marc Yor (3, 4)

1 IECN - Institut Élie Cartan de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 IUF - Institut universitaire de France

We obtain the Laplace transform and integrability properties of the integral over $\Bbb R_+$ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new element to the list of already studied Brownian perpetuities

Mots clés: Bessel-McDonald functions; Sturm-Liouville equation; perpetuities

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Bernard Roynette, Marc Yor. An interesting family of Black-Scholes perpetuities. 2008. ⟨hal-00344713⟩