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Bounds for the American perpetual put on a stock index

Part of: Markov processes Applications Mathematical economics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

V. Paulsen
V. Paulsen*
Affiliation:
Universität Kiel
*
∗ Postal address: Universität Kiel, Mathematisches Seminar, Ludewig Meyn Str. 4, D-24098 Kiel, Germany. Email address: paulsen@math.uni-kiel.de
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Abstract

Let us consider n stocks with dependent price processes each following a geometric Brownian motion. We want to investigate the American perpetual put on an index of those stocks. We will provide inner and outer boundaries for its early exercise region by using a decomposition technique for optimal stopping.

Keywords

mathematical financeoptimal stoppingAmerican optionindex optionearly exercise region

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 91B24: Price theory and market structure 62P05: Applications to actuarial sciences and financial mathematics 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 55 - 66
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

Beibel, M., and Lerche, H. R. (1997). A new look at optimal stopping problems related to mathematical finance. Statist. Sinica 7, 93–108.Google Scholar
Broadie, M., and Detemple, J. (1997). The valuation of American options on multiple assets. Math. Finance 7, 241–286.CrossRefGoogle Scholar
Karatzas, I., and Shreve, S. E. (1998). Methods of Mathematical Finance. Springer, New York.Google Scholar
Lamperton, D., and Lapeyre, B. (1993). Hedging index options with few assets. Math. Finance 3, 25–41.CrossRefGoogle Scholar
McKean, H. P. (1965). A free boundary problem for the heat equation arising from a problem in mathematical economics. Indust. Management Rev. 6, 32–39.Google Scholar
Musiela, M., and Rutkowski, M. (1997). Martingale Methods in Financial Modelling. Springer, New York.CrossRefGoogle Scholar