On the American option problem

Peskir, Goran (2005) On the American option problem. Mathematical Finance, 15 (1). pp. 169-181. ISSN 0960-1627

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Abstract

We show how the change-of-variable formula with local time on curves derived recently in Peskir (2002) can be used to prove that the optimal stopping boundary for the American put option can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation. This settles the question raised in Myneni (1992) and dating back to McKean (1965).

Item Type: Article
Uncontrolled Keywords: American put option, arbitrage-free price, optimal stopping, smooth fit, geometric Brownian motion, free-boundary problem, nonlinear integral equation, local time-space calculus, curved boundary
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 45 Integral equations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 91 Game theory, economics, social and behavioral sciences
Depositing User: Ms Lucy van Russelt
Date Deposited: 21 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/408

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