Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations
type: Item
instance of: scholarly article
title: Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations
zbMATH Open document ID: 1447.91173
author: Emmanuel Gobet
author: Isaque Pimentel
author: Xavier Warin
published in: Finance and Stochastics
publication date: 2020-08-03T00:00:00Z
review text: The authors consider the valuation/hedging policies minimising the residual tracking error in discrete-time hedging. They evaluate the risk between trading dates through a function penalising profits and losses asymmetrically. After deriving the asymptotics from a discrete-time risk measurement for a large number of trading dates, they derive the optimal strategies minimising the asymptotic risk in a continuous-time setting. They characterise optimality through a class of fully nonlinear partial differential equations. Numerical experiments show that the optimal strategies associated with the discrete and the asymptotic approaches coincide asymptotically.
reviewed by: George Stoica
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 35Q91
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 91G60
zbMATH DE Number: 7227000
zbMATH Keywords: hedging
zbMATH Keywords: asymmetric risk
zbMATH Keywords: fully nonlinear parabolic PDE
zbMATH Keywords: regression Monte Carlo
describes a project that uses: StOpt
MaRDI profile type: Publication
full work available at URL: s00780-020-00428-1
OpenAlex ID: W2943323028
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DOI: 10.1007/S00780-020-00428-1
description: scientific article; zbMATH DE number 7227000