Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation
AbstractWe solve the optimal asset allocation problem using a mean variance approach. The original mean variance optimization problem can be embedded into a class of auxiliary stochastic linear-quadratic (LQ) problems using the method in Zhou and Li (2000) and Li and Ng (2000). We use a finite difference method with fully implicit timestepping to solve the resulting nonlinear Hamilton-Jacobi-Bellman (HJB) PDE, and present the solutions in terms of an efficient frontier and an optimal asset allocation strategy. The numerical scheme satisfies sufficient conditions to ensure convergence to the viscosity solution of the HJB PDE. We handle various constraints on the optimal policy. Numerical tests indicate that realistic constraints can have a dramatic effect on the optimal policy compared to the unconstrained solution.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 34 (2010)
Issue (Month): 2 (February)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jedc
Optimal control Mean variance tradeoff HJB equation Viscosity solution;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Damgaard, Anders, 2006. "Computation of reservation prices of options with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 415-444, March.
- Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
- Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
- Merton, Robert C., 1971.
"Optimum consumption and portfolio rules in a continuous-time model,"
Journal of Economic Theory,
Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
- Gerrard, Russell & Haberman, Steven & Vigna, Elena, 2004. "Optimal investment choices post-retirement in a defined contribution pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 321-342, October.
- Chellathurai, Thamayanthi & Draviam, Thangaraj, 2007. "Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2168-2195, July.
- A. C. Belanger & P. A. Forsyth & G. Labahn, 2009. "Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 451-496.
- Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2004.
"A geometric approach to multiperiod mean variance optimization of assets and liabilities,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 28(6), pages 1079-1113, March.
- Markus LEIPPOLD & Fabio TROJANI & Paolo VANINI, 2002. "A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities," FAME Research Paper Series rp48, International Center for Financial Asset Management and Engineering.
- Nguyen, Pascal & Portait, Roland, 2002. "Dynamic asset allocation with mean variance preferences and a solvency constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 11-32, January.
- Munk, Claus, 2000. "Optimal consumption/investment policies with undiversifiable income risk and liquidity constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(9), pages 1315-1343, August.
- Chiu, Mei Choi & Li, Duan, 2006. "Asset and liability management under a continuous-time mean-variance optimization framework," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 330-355, December.
- Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
- Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
- Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.