ISSN:
1432-1122
Schlagwort(e):
Key words:Levy processes, martingales with stationary increments, forward-start-options JEL classification: G13 Mathematics Subject Classification (1991):90A09, 60J60, 60H30
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
,
Wirtschaftswissenschaften
Notizen:
Abstract. In this note, we prove that under some minor conditions on $\sigma$ , if a martingale $X_t = \int_0^t \sigma_u dW_u $ satisfies, for every given pair $u \geq 0, \, \xi \geq 0$ , $X_{u+\xi}-X_u{\mathop{=}^{\mathrm{(law)}}} X_{\xi},$ then necessarily, $|\sigma_u|$ is a constant and X is a constant multiple of a Brownian motion, thus providing a partial analogue of Lévy's characterisation of Brownian motion. In the introduction we explain why this theorem is a reason for considering Lévy processes in finance.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/s007800050047
Permalink
