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A free boundary problem coming from the perpetual American call options with utility

Published online by Cambridge University Press:  22 November 2012

SONG LIPING  and
YU WANGHUI
SONG LIPING
Affiliation:
School of Mathematic Science, Soochow University, Suzhou 215006, China email: [email protected] Research Center of Financial Engineering, Soochow University, Suzhou 215006, China email: [email protected] Department of Mathematics, Putian University, Putian 351100, China
YU WANGHUI
Affiliation:
School of Mathematic Science, Soochow University, Suzhou 215006, China email: [email protected] Research Center of Financial Engineering, Soochow University, Suzhou 215006, China email: [email protected]
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Abstract

A free boundary problem, which comes from the model of the perpetual American call options with utility functions in financial market, is investigated. It is a degenerative parabolic free boundary problem and is studied by the line method. The existence, regularity and uniqueness of the solution as well as some properties of the free boundary are established.

Keywords

Free boundary problemAmerican call optionsUtility function
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 2 , April 2013 , pp. 231 - 271
Copyright
Copyright © Cambridge University Press 2012

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