Optimal portfolios when stock prices follow an exponential Lévy process
type: Item
instance of: scholarly article
title: Optimal portfolios when stock prices follow an exponential Lévy process
zbMATH Open document ID: 1051.60049
author: Susanne Emmer
author: Claudia Klüppelberg
published in: Finance and Stochastics
publication date: 2004-11-24T00:00:00Z
review text: The authors investigate portfolio optimization problems when the price processes are governed by general exponential Lévy processes, comparing the optimal solutions with variance and value-at-risk as risk measures, respectively. They introduce a multivariate Lévy Black-Scholes model and calculate the terminal wealth of a portfolio and its moments provided they exist. Then these results are used for a portfolio optimization that consists of maximizing the expected terminal wealth of a portfolio within a well-defined set of strategies under some constraint on the variance. The notion of capital-at-risk (CaR) is introduced, which is defined via a low quantile (value-at-risk) of the wealth process, and methods for its calculation and approximations are discussed. The portfolios, where the variance is replaced by CaR, are optimized. Real life examples as the normal inverse Gaussian and variance gamma model are worked out. Closed form analytic solutions are not obtained, but the optimization problem is solved by an approximation and numerical algorithm.
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 91B70
zbMATH DE Number: 2118687
zbMATH Keywords: capital-at-risk
zbMATH Keywords: downside risk measure
zbMATH Keywords: exponential Lévy process
zbMATH Keywords: portfolio optimization
zbMATH Keywords: stochastic exponential
zbMATH Keywords: value-at-risk
zbMATH Keywords: weak limit law
zbMATH Keywords: Lévy process
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s00780-003-0105-4
OpenAlex ID: W2004486733
DOI: 10.1007/S00780-003-0105-4
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description: scientific article; zbMATH DE number 2118687