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Mathematical Problems in Engineering
Volume 2013, Article ID 932579, 10 pages
http://dx.doi.org/10.1155/2013/932579
Research Article

Dividends Sharing Convertible Bonds Pricing and Numerical Evaluation

1Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
2School of Mathematics, Shandong University, Jinan 250100, China

Received 23 January 2013; Accepted 23 April 2013

Academic Editor: Guangchen Wang

Copyright © 2013 Xu Guo and Haiyang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The convertible bond is becoming one of the most important financial instruments for the company to raise capital fund since it was first issued by American New York Erie Company in 1843. In this paper, it is the first time to study the pricing problem for convertible bond whose underlying stocks pay dividends via the reflected backward stochastic differential equations. Associating the solutions of reflected BSDEs with the obstacle problems for nonlinear parabolic PDEs, we establish the pricing formulas for convertible bonds with continuous and discrete dividends by means of the viscosity solutions for some PDEs. Besides, we also derive the price of convertible bonds with higher borrowing rate which is realistic in the financial market. Then the numerical evaluations are provided by the radial basis functions method. Moreover, we discuss the influence of dividends paying as well as higher borrowing rate on the convertible bond price at last.