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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: lipingsong@126.com Research Center of Financial Engineering, Soochow University, Suzhou 215006, China email: whyu@suda.edu.cn Department of Mathematics, Putian University, Putian 351100, China
YU WANGHUI
Affiliation:
School of Mathematic Science, Soochow University, Suzhou 215006, China email: lipingsong@126.com Research Center of Financial Engineering, Soochow University, Suzhou 215006, China email: whyu@suda.edu.cn
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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

Information

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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References

Dewynne, J. N., Howison, S. D., Rupf, I. & Wilmott, P. (1993) Some mathematical results in the pricing of American options. Eur. J. Appl. Math. 4, 381–398.CrossRefGoogle Scholar
Fleming, W. H. & Soner, H. M. (2006) Controlled Markov Processes and Viscosity Solutions, Springer, New York.Google Scholar
Friedman, A. (1988) Variational Principles and Free-Boundary Problems, John Wiley, Hoboken, NJ.Google Scholar
Grasselli, M. & Henderson, V. (2009) Risk aversion and block exercise of executive stock options. J. Econ. Dyn. Control 33 (1), 109–127.CrossRefGoogle Scholar
Jaillet, P., Lamberton, D. & Lapeyre, B. (1990) Variational inequalities and pricing of American options. Acta Appl. Math. 21, 263–289.CrossRefGoogle Scholar
Jiang, L. (2005) Mathematical Modeling and Methods of Option Pricing, World Scientific Publication, Hackensack, NJ.CrossRefGoogle Scholar
Leung, T. & Sircar, R. (2009) Accounting for risk aversion, vesting, job termination risk and multiple exercises in valuation of employee stock options. Math. Finance 19 (1), 99–128.CrossRefGoogle Scholar
Pham, H. (2009) Continuous-Time Stochastic Control and Optimization with Financial Applications, Springer-Verlag, Berlin, Germany.CrossRefGoogle Scholar
Rogers, L. C. G. & Scheinkman, J. (2007) Optimal exercise of executive stock options. Finanae Stoch. 11, 357–372.CrossRefGoogle Scholar
Song, L. & Yu, W. (2011) A parabolic variational inequality related to the perpetual American executive stock options. Nonlinear Anal. 74, 6583–6600.CrossRefGoogle Scholar
Wilmott, P., Dewynne, J. N. & Howison, S. D. (1992) Option Pricing: Mathematical Models and Computation, Oxford Financial Press, Oxford, UK.Google Scholar