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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 3
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Original Articles

A free boundary problem arising from pricing convertible bond

Zhou Yang Department of Mathematics, South China Normal University, Guangzhou 510631, PR China
&
Fahuai Yi Department of Mathematics, South China Normal University, Guangzhou 510631, PR ChinaCorrespondence[email protected]
Pages 307-323 | Received 21 May 2009, Accepted 22 Nov 2009, Published online: 05 Mar 2010
 
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Abstract

In this article we study the behaviours of the optimal conversion boundary (i.e. free boundary) of an American-style convertible bond with finite horizon (i.e. parabolic case). We prove the existence and the uniqueness of the strong solution of the problem and the boundedness and smoothness of the free boundary. Moreover, we characterize the free boundary's start point and present two numerical results.

AMS Subject Classifications:

Acknowledgements

The project is supported by NNSF of China (No. 10971073, No. 10801056 and No. 10901060) and NNSF of GuangDong province (No. 9451063101002091).

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