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Abstract

Symmetry Analysis of the Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics †

by
Maluti Kgarose
* and
Jacob Matshwenyego Manale
*
Department of Mathematical Sciences, University of South Africa, Roodepoort 1709, South Africa
*
Authors to whom correspondence should be addressed.
†
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)
Versions Notes
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

  1. Heath, D.; Platen, E.; Schweizer, M. Numerical Comparison of Local Risk-Minimisation and Meanvariance Hedging; Australian National University: Canberra, Australia, 1999. [Google Scholar]
  2. 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]
  3. 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 Style

Kgarose, 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

APA Style

Kgarose, M., & Manale, J. M. (2018). Symmetry Analysis of the Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics. Proceedings, 2(1), 8. https://doi.org/10.3390/proceedings2010008

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