Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T14:55:55.717Z Has data issue: false hasContentIssue false

POLYNOMIAL BOUNDS FOR SOLUTIONS TO BOUNDARY VALUE AND OBSTACLE PROBLEMS WITH APPLICATIONS TO FINANCIAL DERIVATIVE PRICING

Published online by Cambridge University Press:  02 November 2017

LOUIS BHIM*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia email louis.bhim@gmail.com
Rights & Permissions [Opens in a new window]

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Abstracts of Australasian PhD Theses
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Bensoussan, A. and Lions, J.-L., Applications of Variational Inequalities in Stochastic Control (North-Holland, New York, 1982).Google Scholar
Bhim, L. and Kawai, R., ‘Smooth upper bounds for the price of American style options’, Int. J. Theor. Appl. Finance (2017), to appear.Google Scholar
Bhim, L. and Kawai, R., ‘Polynomial upper and lower bounds for financial derivative price functions under regime-switching’, J. Comput. Finance 22(2) (2018), to appear.Google Scholar
Friedman, A., Variational Principles and Free Boundary Problems (Wiley-Interscience, New York, 1982).Google Scholar
Haugh, M. B. and Kogan, L., ‘Pricing American options: a duality approach’, Oper. Res. 52(2) (2004), 258270.Google Scholar
Kawai, R., ‘Explicit hard bounding functions for boundary value problems for elliptic partial differential equations’, Comput. Math. Appl. 70(12) (2015), 28222837.Google Scholar
Kawai, R. and Kashima, K., ‘On weak approximation of stochastic differential equations through hard bounds by mathematical programming’, SIAM J. Sci. Comput. 35(1) (2013), A1A25.Google Scholar
Kinderlehrer, D. and Stampacchia, G., An Introduction to Variational Inequalities and Their Applications (Academic Press, London, 2000).Google Scholar
Löfberg, J., ‘Pre- and post-processing sum-of-squares programs in practice’, IEEE Trans. Automat. Control 54(5) (2009), 10071011.Google Scholar
Rogers, L. C. G., ‘Monte Carlo valuation of American options’, Math. Finance 12 (2002), 271286.Google Scholar
Tütüncü, R. H., Toh, K. C. and Todd, M. J., ‘Solving semidefinite-quadratic-linear programs using SDPT3’, Math. Program. Ser. B 95 (2003), 189217.Google Scholar