Publication: Numerical Solution of the Hamilton Jacobi Bellman Formulation for Continuous time mean variance asset allocation

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Title	Numerical Solution of the Hamilton Jacobi Bellman Formulation for Continuous time mean variance asset allocation
Authors/Editors*	J. Wang, P.A. Forsyth
Where published*	Working paper
How published*	Technical Report
Year*	2008
Volume
Number
Pages	38
Publisher
Keywords	Optimal control, mean variance, HJB equation, viscosity solution
Link	www.scicom.uwaterloo.ca/~paforsyt/mean_variance.pdf
Abstract	We 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 \citep{zhou2000, Li2000}. We use a finite difference method with fully implicit timestepping to solve the resulting non-linear 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.