The Convexity of the Free Boundary for a Parabolic Free Boundary Problem
AbstractIn this paper, we study a parabolic free boundary problem which shows that the solutions of this free boundary problem are increasing functions. Furthermore, we provide a rigorous veri?cation for that the free boundary for this problem is concave. As an application to the American option pricing problem, our results imply that the early exercise boundary of an American call is a strictly decreasing concave function. This result provides a useful information to obtain an asymptotic formula for the early exercise boundary.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1304.5337.
Date of creation: Apr 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-27 (All new papers)
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- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
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