On lower partial moments for the investment portfolio with variance-gamma distributed returns
type: Item
instance of: scholarly article
title: On lower partial moments for the investment portfolio with variance-gamma distributed returns
zbMATH Open document ID: 1490.60042
published in: Lithuanian Mathematical Journal
publication date: 2022-03-14T00:00:00Z
review text: The author considers a portfolio of investments \(x_1,\ldots, x_n\) into \(n\) financial assets with value \(X=\sum_{j=1}^n x_jR_j\), where the returns \(R_j\) are variance-gamma distributed, i.e.,\ \(R_j=r_j+\theta_jX_j+\sigma_j\sqrt{X_j}N_j\) with \(r_j,\theta_j\in\mathbb R\), \(\sigma_j\geq0\), and gamma distributed random variables \(X_j\) independent of the (possibly correlated) standard normal distributed random variables \(N_j\). The author derives analytic expressions of the lower partial moments of \(X\) in terms of generalized hypergeometric functions, and as a consequence provides formulas for the value at risk, expected shortfall, and the target semideviation of \(X\).
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 33C90
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 91G70
zbMATH DE Number: 7488658
zbMATH Keywords: variance-gamma distribution
zbMATH Keywords: lower partial moment
zbMATH Keywords: generalized hypergeometric function
zbMATH Keywords: value at risk
zbMATH Keywords: expected shortfall
zbMATH Keywords: semideviation
author: Roman Ivanov
describes a project that uses: BRENT
MaRDI profile type: Publication
full work available at URL: s10986-021-09547-4
OpenAlex ID: W4205790981
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DOI: 10.1007/S10986-021-09547-4
description: scientific article; zbMATH DE number 7488658