Efficient hedging with coherent risk measure
type: Item
instance of: scholarly article
title: Efficient hedging with coherent risk measure
zbMATH Open document ID: 1085.91032
author: Yumiharu Nakano
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
full work available at URL: http://hdl.handle.net/2115/69271
review text: According to the definition of Föllmer and Leukert, the shortfall risk is the expectation of the shortfall weighted by a loss function, and looked for strategies that minimize the shortfall risk under a capital constraint. In order to measure the shortfall risk, the author uses coherent risk measures proposed by Artzener, Delbaen, Eber and Heath. On the basis of a representation result in the case of coherent \(L^1\)-lower-semicontinuous risk measures, it is proved that, for a given contingent claim \(H\), the optimal strategy consists in hedging a modified claim \(\phi H\), for some randomized test \(\phi\) (i.e. \(\phi:\Omega\to[0,1]\), with \(\phi\) measurable, given the probability space \((\Omega, F,P)\)). Finally some cases involving special coherent risk measures are considered, as the worst conditional expectation.
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 2082148
zbMATH Keywords: hedging
zbMATH Keywords: shortfall risk
zbMATH Keywords: efficient hedging
zbMATH Keywords: coherent risk measure
zbMATH Keywords: randomized test
zbMATH Keywords: Neyman-Pearson lemma
zbMATH Keywords: worst
zbMATH Keywords: conditional expectation
reviewed by: Emilia Di Lorenzo
MaRDI profile type: Publication
OpenAlex ID: W1978849664
cites work: Coherent measures of risk
cites work: Q4550909
cites work: Efficient hedging: cost versus shortfall risk
cites work: On the worst conditional expectation.
cites work: Q4548486
cites work: Q4048357
DOI: 10.1016/J.JMAA.2004.01.010
description: scientific article; zbMATH DE number 2082148