American options with guarantee -- a class of two-sided stopping problems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1288.60050
author: Sören Christensen
author: Albrecht Irle
publication date: 2013-10-25T00:00:00Z
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 6220106
zbMATH Keywords: optimal stopping
zbMATH Keywords: two-sided strategies
zbMATH Keywords: diffusions
zbMATH Keywords: Lévy processes
MaRDI profile type: Publication
full work available at URL: strm.2013.1122
OpenAlex ID: W1970811103
DOI: 10.1524/STRM.2013.1122
title: American options with guarantee -- a class of two-sided stopping problems
published in: Statistics \& Risk Modeling
review text: The paper deals with a class of two-sided stopping problems. If the payoff depends on the starting point then the classical stopping theory for one-dimensional processes does not work. The authors suggest in such a case to embed the optimal stopping problem to a two-dimensional one. One can look upon this situation as on the American options with guarantee where the guaranteed payoff is a fraction of the starting price. At first, the authors assume that the driving process is a diffusion. This assumption allows to apply the harmonic-functions techniques and to look for the explicit solution of two differential equations characterizing the optimal strategy. Then they study the case of Lévy processes where the explicit solution is obtained for spectrally negative processes applying scale functions.
reviewed by: Tomáš Cipra
description: scientific article; zbMATH DE number 6220106