Dynamic Mean-Variance Portfolio Selection with No-Shorting Constraints
SIAM Journal on Control and Optimization
Convex Optimization
A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion
SIAM Journal on Scientific Computing
A Semi-Lagrangian Approach for Natural Gas Storage Valuation and Optimal Operation
SIAM Journal on Scientific Computing
Maximal Use of Central Differencing for Hamilton-Jacobi-Bellman PDEs in Finance
SIAM Journal on Numerical Analysis
Regularized robust optimization: the optimal portfolio execution case
Computational Optimization and Applications
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The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a linear-quadratic (LQ) optimal stochastic control problem. A semi-Lagrangian scheme is used to solve the resulting nonlinear Hamilton-Jacobi-Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparison property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.