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On predicting the ultimate maximum for exponential Lévy processes

   
@article{ECP1805,
	author = {Katsunori Ano and Roman Ivanov},
	title = {On predicting the ultimate maximum for exponential Lévy processes},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {optimal stopping; exponential Lévy process; predicting; selling of asset; utility function},
	abstract = {
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.
},
	pages = {no. 46, 1-9},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-1805},    
        url = {http://ecp.ejpecp.org/article/view/1805}}