Far-from-expiry behavior of the American put option on a dividend-paying asset

Chen, Xinfu; Cheng, Huibin; Chadam, John

doi:10.1090/S0002-9939-2010-10516-6

Far-from-expiry behavior of the American put option on a dividend-paying asset
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by Xinfu Chen, Huibin Cheng and John Chadam PDF

Proc. Amer. Math. Soc. 139 (2011), 273-282 Request permission

Abstract:

We provide a rigorous proof of sharp estimates for the long time behavior of the early exercise boundary and the price for an American put option on a dividend-paying asset that follows a geometric Brownian motion.

References

Cheonghee Ahn, Hi Jun Choe, and Kijung Lee, A long time asymptotic behavior of the free boundary for an American put, Proc. Amer. Math. Soc. 137 (2009), no. 10, 3425–3436. MR 2515412, DOI 10.1090/S0002-9939-09-09900-6
Xinfu Chen and John Chadam, A mathematical analysis of the optimal exercise boundary for American put options, SIAM J. Math. Anal. 38 (2006/07), no. 5, 1613–1641. MR 2286022, DOI 10.1137/S0036141003437708
Xinfu Chen, Huibin Cheng and J. Chadam, Non-convexity of the optimal exercise boundary for an American put option on a dividend-paying asset, preprint, submitted for publication.

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Additional Information

Xinfu Chen
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
MR Author ID: 261335
Huibin Cheng
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
John Chadam
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Received by editor(s): June 1, 2009
Received by editor(s) in revised form: December 22, 2009, and March 3, 2010
Published electronically: July 12, 2010
Additional Notes: The first author acknowledges support from NSF grant DMS-0504691.
The second and third authors acknowledge support from NSF grant DMS-0707953.
The authors would like to thank the referees for their comments, which have improved the presentation of the results.
Communicated by: Walter Craig
Journal: Proc. Amer. Math. Soc. 139 (2011), 273-282
MSC (2010): Primary 35R35, 91G20, 91G80
DOI: https://doi.org/10.1090/S0002-9939-2010-10516-6
MathSciNet review: 2729089