A parabolic variational inequality arising from the valuation of strike reset options
type: Item
instance of: scholarly article
title: A parabolic variational inequality arising from the valuation of strike reset options
zbMATH Open document ID: 1110.35040
author: Zhou Yang
author: Min Dai
author: Fahuai Yi
published in: Journal of Differential Equations
publication date: 2007-01-09T00:00:00Z
review text: The authors study a parabolic variational inequality problem \[ \begin{aligned} &\partial_t V-\frac{\sigma^2}2S^2\partial_{SS}V+rV\geq 0,\;V(S,\tau)\geq SP(\tau),\;S>0,\;0<\tau\leq T,\\ &\biggl[\partial_t V-\frac{\sigma^2}2S^2\partial_{SS}V+rV\biggr][V-SP(\tau)]=0,\;V(S,0)=(1-S)^+, \end{aligned} \] where \(V(S,\tau)\) is the option value. The paper establishes the existence and uniqueness of \(W_p^{1,2}\) solution and the boundedness and \(C^\infty\) smoothness of the free boundary. The monotonicity of the free boundary is proved in some situations.
Mathematics Subject Classification ID: 35K85
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 5083417
zbMATH Keywords: option prising
zbMATH Keywords: American option
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: monotonicity of the free boundary
reviewed by: Igor Bock
MaRDI profile type: Publication
full work available at URL: j.jde.2006.07.026
OpenAlex ID: W2073467017
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DOI: 10.1016/J.JDE.2006.07.026
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description: scientific article; zbMATH DE number 5083417