Optimal approximations for risk measures of sums of lognormals based on conditional expectations
type: Item
instance of: scholarly article
title: Optimal approximations for risk measures of sums of lognormals based on conditional expectations
zbMATH Open document ID: 1154.91021
published in: Journal of Computational and Applied Mathematics
publication date: 2008-10-22T00:00:00Z
review text: The distribution function (d.f.) of the sum \(S=\sum_{i=1}^n\alpha_i e^{Z_i}\), where \(\alpha_i>0\) and the vector \((Z_1,Z_2,\ldots,Z_n)\) has a multivariate normal distribution, is studied. D.f. of \(S\) is approximated by the d.f. of conditional expectation \(E[S/\Lambda]\) with respect to a conditioning random variable \(\Lambda\). An appropriate choice of \(\Lambda\) leads to a comonotonicity of conditional vector and this helps to approximate risk measures related to the d.f. of \(S\) by the corresponding risk measures of \(E[S/\Lambda]\). Globally optimal choces of \(\Lambda\) connected with ``Taylor-based'' and ``maximal variance'' approximations are considered. Locally optimal choces of \(\Lambda\) are studied as well, they are connected with ``CTE\(_{p}\)-based'' and an ``asymptotically optimal'' approximations. Applications to discounting, compounding and to the pricing of Asian options are presented.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60Exx
zbMATH DE Number: 5355644
zbMATH Keywords: Comonotonicity
zbMATH Keywords: lognormal distribution
zbMATH Keywords: maximal variance
zbMATH Keywords: conditional expectation
zbMATH Keywords: risk measures
author: Steven Vanduffel
author: Xinliang Chen
author: J. Dhaene
author: Marc J. Goovaerts
author: Luc Henrard
author: Rob Kaas
describes a project that uses: QRM
MaRDI profile type: Publication
full work available at URL: j.cam.2007.10.050
OpenAlex ID: W3124434029
cites work: Asymptotics of sums of lognormal random variables with Gaussian copula
cites work: Benchmarking, portfolio insurance and technical analysis: a Monte Carlo comparison of dynamic strategies of asset allocation
cites work: On dynamic investment strategies
cites work: Bounds for Asian basket options
cites work: Comonotonic bounds on the survival probabilities in the Lee--Carter model for mortality projection
cites work: The concept of comonotonicity in actuarial science and finance: theory.
cites work: The concept of comonotonicity in actuarial science and finance: applications.
cites work: Risk Measures and Comonotonicity: A Review
cites work: Some results on the CTE-based capital allocation rule
cites work: Martingales and arbitrage in multiperiod securities markets
cites work: Martingales and stochastic integrals in the theory of continuous trading
cites work: Ruined moments in your life: how good are the approximations?
cites work: Upper and lower bounds for sums of random variables
cites work: Optimal reinsurance in relation to ordering of risks
cites work: Q5706744
cites work: The value of an Asian option
cites work: Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables
cites work: The hurdle-race problem.
cites work: Bounds for the price of discrete arithmetic Asian options
DOI: 10.1016/J.CAM.2007.10.050
description: scientific article; zbMATH DE number 5355644