The minimal entropy martingale measures for geometric Lévy processes
type: Item
instance of: scholarly article
title: The minimal entropy martingale measures for geometric Lévy processes
zbMATH Open document ID: 1035.60040
author: Tsukasa Fujiwara
author: Yoshio Miyahara
published in: Finance and Stochastics
publication date: 2004-03-16T00:00:00Z
review text: The authors establish the existence of the minimal entropy martingale measures (MEMMs) for the geometric Lévy processes \(\tilde{S}_t\) and show that the MEMM can be defined by means of the Esscher transformation of the return process for \(\tilde{S}_t\) which gives an explicit representation of the MEMM. A criterion is given for judging when conditions of the main theorems are fulfilled. For instance, compound Poisson processes, stable processes and variance gamma processes are good enough. It is also proved that MEMM price is the limit of the utility indifference price as the risk aversion parameter tends to 0.
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 2059115
zbMATH Keywords: geometric Lévy processes
zbMATH Keywords: (local) martingale measures
zbMATH Keywords: minimal entropy
zbMATH Keywords: Esscher transformation
zbMATH Keywords: utility indifference price
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s007800200097
OpenAlex ID: W2017392078
DOI: 10.1007/S007800200097
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description: scientific article; zbMATH DE number 2059115