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Journal of Optimization Theory and Applications

, Volume 179, Issue 1, pp 311–331 | Cite as

Power Penalty Approach to American Options Pricing Under Regime Switching

  • Kai ZhangEmail author
  • Xiaoqi Yang
Article
  • 256 Downloads

Abstract

This work aims at studying a power penalty approach to the coupled system of differential complementarity problems arising from the valuation of American options under regime switching. We introduce a power penalty method to approximate the differential complementarity problems, which results in a set of coupled nonlinear partial differential equations. By virtue of variational inequality theory, we establish the unique solvability of the system of differential complementarity problems. Moreover, the convergence property of this power penalty method in an appropriate infinite-dimensional space is explored, where an exponential convergence rate of the power penalty method is established and the monotonic convergence of the penalty method with respect to the penalty parameter is shown. Finally, some numerical experiments are presented to verify the convergence property of the power penalty method.

Keywords

American option pricing Regime switching Differential complementarity problem Power penalty method Convergence analysis 

Mathematics Subject Classification

65N12 65K10 91B28 

Notes

Acknowledgements

The authors would like to thank the anonymous referees and the editor for their helpful comments and suggestions toward the improvement of this paper. Kai Zhang wishes to thank the support from the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (Grant No. 14JJD790041). Project 11001178 is partially supported by National Natural Science Foundation of China.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shenzhen Audencia Business SchoolShenzhen UniversityShenzhenChina
  2. 2.Department of Applied MathematicsHong Kong Polytechnic UniversityHung HomHong Kong

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