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

Part of: Probabilistic methods, simulation and stochastic differential equations Mathematical finance

Published online by Cambridge University Press:  02 November 2017

LOUIS BHIM
LOUIS BHIM*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia email louis.bhim@gmail.com
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Abstract

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Keywords

obstacle problemoptimal stoppingdual approachfree-boundary problempolynomial boundsAmerican option priceregime switching

MSC classification

Primary: 65C99: None of the above, but in this section
Secondary: 65K15: Numerical methods for variational inequalities and related problems 90C22: Semidefinite programming 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 174 - 176
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), 258–270.Google Scholar
Kawai, R., ‘Explicit hard bounding functions for boundary value problems for elliptic partial differential equations’, Comput. Math. Appl. 70(12) (2015), 2822–2837.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), A1–A25.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), 1007–1011.Google Scholar
Rogers, L. C. G., ‘Monte Carlo valuation of American options’, Math. Finance 12 (2002), 271–286.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), 189–217.Google Scholar