Regularity of the free boundary for the American put option

Xinfu Chen; Huibin Cheng

doi:10.3934/dcdsb.2012.17.1751

Article Contents

2012, Volume 17, Issue 6: 1751-1759. Doi: 10.3934/dcdsb.2012.17.1751

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Regularity of the free boundary for the American put option

Xinfu Chen^1, and
Huibin Cheng^2,

1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
2.
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1

Received: August 31, 2011

Revised: October 31, 2011

Published: August 2012

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Abstract

We show the free boundary of the American put option with dividend payment is $C^{\infty}$.

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Mathematics Subject Classification: Primary: 35R35, 35B65; Secondary: 91G50.

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References

[1]	E. Bayraktar and H. Xing, Analysis of the optimal exercise boundary of American option for jump diffusions, SIAM. J. Math. Anal., 41 (2009), 825-860.doi: 10.1137/080712519.
[2]	A. Bensoussan, On the theory of option pricing, Acta Appl. Math., 2 (1984), 139-158.
[3]	A. Bensoussan & J.-L. Lions, "Application of Variational Inequalities in Stochastic Control," Studies in Mathematics and its Applications, 12, North-Holland Publishing Co., Amsterdam-New York, 1982.
[4]	X. Chen and J. Chadam, A mathematical analysis of the optimal boundary for American put options, SIAM J. Math. Anal., 38 (2006/07), 1613-1641.
[5]	Xinfu Chen and J. Chadam, Analytic and numerical approximations for the early exercise boundary for American put options, Dyn. Cont. Disc. and Impulsive Sys., 10 (2003), 649-657.
[6]	Xinfu Chen, J. Chadam and Huibin Cheng, Non-convexity of the optimal exercise boundary for an American put option on a dividend-paying asset, Mathematical Finance, to appear. Available from: http://www.pitt.edu/~chadam/papers/LargeDNonConvex.pdf.
[7]	Xinfu Chen, J. Chadam, L. Jiang and W. Zheng, Convexity of the exercise boundary of the American put option on a zero dividend asset, Math. Finance, 18 (2008), 185-197.doi: 10.1111/j.1467-9965.2007.00328.x.
[8]	A. Friedman, "Variational Principles and Free Boundary Problems," A Wiley-Interscience Publication, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982.
[9]	A. Friedman, "Partial Diffferential Equations of Parabolic Type," Prentice-Hall, 1964.
[10]	A. Friedman, Analyticity of the free boundary for the Stefan problem, Arch. Rational Mech. Anal., 61 (1976), 97-125.doi: 10.1007/BF00249700.
[11]	L. Jiang, Existence and differentiability of the solution of a two phase Stefan problem for quasi-linear parabolic equations, Chinese Math. Acta, 7 (1965), 481-496.
[12]	D. Lamberton and M. Mikou, The critical price for the American put in an exponential Lévy model, Finance Stoch., 12 (2008), 561-581.doi: 10.1007/s00780-008-0073-9.
[13]	P. Laurence and S. Salsa, Regularity of the free boundary of an American option on several assets, Comm. on Pure and Appl. Math., 62 (2009), 969-994.doi: 10.1002/cpa.20268.
[14]	H. P. McKean, Jr., Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics, Industrial Management Review, 6 (1965), 32-39.
[15]	P. van Moerbeke, On optimal stopping and free boundary problems, Arch. Rational Mech. Anal., 60 (1975/76), 101-148.
[16]	C. Yang, L. Jiang and B. Bian, Free boundary and American option in a jump-diffusion model, Euro. J. of Applied Mathematics, 17 (2006), 95-127.doi: 10.1017/S0956792505006340.
[17]	P. Wilmott, J. Dewynne and S. Howison, "The Mathematics of Financial Derivatives. A Student Introduction," Cambridge University Press, Cambridge, 1995.