| Título: | On predicting the ultimate maximum for exponential Lévy processes |
| Autores: |
Ano, Katsunori; Shibaura Institute of Technology, Tokyo Ivanov, Roman; Trapeznikov Institute of Control Sciences of RAS, Moscow |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
optimal stopping; exponential Lévy process; predicting; selling of asset; utility function 60G25; 60G51; 60G70 |
| Descripción: | We consider a problem of predicting of the ultimate maximum of the process over a finite interval of time. Mathematically, this problem relates to a particular optimal stopping problem. In this paper we discuss exponential Lévy processes. As the Lévy processes, we discuss $\alpha$-stable Lévy processes, $0<\alpha\leq 2$, and generalized hyperbolic Lévy processes. The method of solution uses the representations of these processes as time-changed Brownian motions with drift. Our results generalize results of papers by Toit and Peskir and by Shiryaev and Xu, and Zhou. |
| Idioma: | Inglés |
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