We develop an efficient method for solving dynamic portfolio selection problems in the presence of transaction cost, liquidity cost and market impact. Our method, based on least-squares Monte Carlo simulation, has no restriction on return dynamics, portfolio constraints, intermediate consumption and investor's objective. We model return dynamics as exogenous state variables and model portfolio weights, price dynamics and portfolio value as endogenous state variables. This separation allows for incorporation of any formation of transaction cost, liquidity cost and market impact. We first perform a forward simulation for both exogenous and endogenous state variables, then use a least-squares regression to approximate the backward recursive dynamic programs on a discrete grid of controls. Finally, we use a local interpolation and an adaptive refinement grid to enhance the optimal allocation estimates. The computational runtime of this framework grows polynomially with dimension. Its viability is illustrated on a realistic portfolio allocation example with twelve risky assets.
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