On predicting the ultimate maximum for exponential Lévy processes
type: Item
instance of: scholarly article
title: On predicting the ultimate maximum for exponential Lévy processes
zbMATH Open document ID: 1255.60066
author: Katsunori Ano
author: Roman Ivanov
published in: Electronic Communications in Probability
publication date: 2012-10-23T00:00:00Z
review text: The authors take exponential Lévy process and consider the probelm of optimal stopping in the interval \([0,T]\) of the ratio of the process itself and its maximal value, and vice versa. More precisely, \(\alpha\)-stable and generalized hyperbolic Lévy processes are studied. This problem corresponds to the linear utility, however, logarithmic utility is considered as well. The optimal solution is trivial, in some sense: it equals the maturity date otherwise it equals the initial date. The advantage of the proofs is that they do not depend on the particular change of time for the underlying process. The application to the selling of assets is discussed.
Mathematics Subject Classification ID: 60G25
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 6098196
zbMATH Keywords: optimal stopping
zbMATH Keywords: exponential Lévy process
zbMATH Keywords: predicting
zbMATH Keywords: selling of asset
zbMATH Keywords: utility function
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: ecp.v17-1805
OpenAlex ID: W2083274879
DOI: 10.1214/ECP.V17-1805
description: scientific article; zbMATH DE number 6098196