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Russian options with a finite time horizon

Part of:Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Erik Ekström
Erik Ekström*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden. Email address: ekstrom@math.uu.se
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Abstract

We investigate the Russian option with a finite time horizon in the standard Black–Scholes model. The value of the option is shown to be a solution of a certain parabolic free boundary problem, and the optimal stopping boundary is shown to be continuous. Moreover, the asymptotic behavior of the optimal stopping boundary near expiration is studied.

Keywords

Optimal stoppingmaximum processoptimal stopping boundaryoptions

MSC classification

Primary:60G40: Stopping times; optimal stopping problems; gambling theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004, pp. 313 - 326
Copyright
Copyright © Applied Probability Trust 2004 

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