Symmetry Analysis of the Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics †
Department of Mathematical Sciences, University of South Africa, Roodepoort 1709, South Africa
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Authors to whom correspondence should be addressed.
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Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Proceedings 2018, 2(1), 8; https://doi.org/10.3390/proceedings2010008
Published: 15 January 2018
(This article belongs to the Proceedings of The First International Conference on Symmetry)
We outline symmetry analysis on the Hamilton-Bellman-Jacobi equation presented by Heath in [1] as an equation for mean-variance hedging and analyzed by Leach in [2] using classical symmetry analysis. We further apply modified symmetry analysis on this equation and compare our analytic results with numerical solutions. We do this by introducing a new infinitesimal parameter into the group generators [3]. This helps us solve the unintegrable solutions usually appearing in invariant solutions.
References
- Heath, D.; Platen, E.; Schweizer, M. Numerical Comparison of Local Risk-Minimisation and Meanvariance Hedging; Australian National University: Canberra, Australia, 1999. [Google Scholar]
- Naicker, V.; Andriopoulos, K.; Leach, P.G.L. Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics. J. Nonlinear Math. Phys. 2005, 12, 268–283. [Google Scholar] [CrossRef]
- Adams, C.; Masebe, T.; Manale, J. Gaussian type differential equation. RECENT ADVANCES in MATHEMATICAL METHODS, MATHEMATICAL MODELS and SIMULATION in SCIENCE and ENGINEERING. In Proceedings of the 2014 International Conference on Mathematical Models and Methods in Applied Sciences, Saint Petersburg, Russia, 23–25 September 2014; p. 28. [Google Scholar]
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MDPI and ACS Style
Kgarose, M.; Manale, J.M. Symmetry Analysis of the Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics. Proceedings 2018, 2, 8. https://doi.org/10.3390/proceedings2010008
AMA Style
Kgarose M, Manale JM. Symmetry Analysis of the Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics. Proceedings. 2018; 2(1):8. https://doi.org/10.3390/proceedings2010008
Chicago/Turabian StyleKgarose, Maluti, and Jacob Matshwenyego Manale. 2018. "Symmetry Analysis of the Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics" Proceedings 2, no. 1: 8. https://doi.org/10.3390/proceedings2010008
