[Paper Review] Efficient Simulation Method for Dynamic Portfolio Selection with Transaction Cost, Liquidity Cost and Market Impact

Rongju Zhang, Nicolas Langrené+4 more|arXiv (Cornell University)|Oct 1, 2016

Monetary Policy and Economic Impact5 references3 citations

TL;DR

This paper proposes a least-squares Monte Carlo framework for dynamic portfolio optimization under transaction costs, liquidity costs, and market impact. By modeling returns as exogenous variables and portfolio weights, prices, and value as endogenous variables, it enables flexible cost modeling and uses regression-based backward induction with adaptive grids to achieve polynomial-time scalability, demonstrated on a 12-asset portfolio.

ABSTRACT

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.

Motivation & Objective

• To address the computational complexity of dynamic portfolio selection under realistic market frictions such as transaction costs, liquidity costs, and market impact.
• To develop a simulation-based method that imposes no restrictions on return dynamics, portfolio constraints, intermediate consumption, or investor objectives.
• To enable flexible modeling of transaction cost, liquidity cost, and market impact structures through a clear separation of exogenous and endogenous state variables.
• To enhance the accuracy of optimal portfolio allocation estimates using local interpolation and adaptive refinement grids in a least-squares regression framework.
• To ensure computational efficiency by achieving polynomial runtime growth with respect to portfolio dimensionality.

Proposed method

• Model returns as exogenous state variables and portfolio weights, asset prices, and portfolio value as endogenous state variables to decouple dynamics from cost structures.
• Perform forward simulation of both exogenous and endogenous state variables to generate sample paths under the specified dynamics.
• Apply least-squares regression on a discrete grid of control variables to approximate the backward recursive dynamic programming solution.
• Use local interpolation to refine allocation estimates at non-grid points, improving solution accuracy without increasing grid size.
• Implement an adaptive refinement grid that focuses computational effort on regions of higher sensitivity or value function curvature.
• Ensure scalability by maintaining polynomial runtime growth with respect to the number of assets and state variables.

Experimental results

Research questions

• RQ1 How can dynamic portfolio optimization be efficiently solved when transaction costs, liquidity costs, and market impact are jointly present?
• RQ2 Can a simulation-based method handle arbitrary return dynamics and portfolio constraints without restrictive assumptions?
• RQ3 How does the separation of exogenous and endogenous state variables enable flexible modeling of complex market frictions?
• RQ4 To what extent does local interpolation and adaptive grid refinement improve the accuracy of optimal portfolio allocation estimates?
• RQ5 What is the computational scalability of the proposed method in high-dimensional portfolio settings?

Key findings

• The proposed method enables dynamic portfolio optimization under general return dynamics and portfolio constraints without restrictive assumptions.
• The separation of exogenous and endogenous state variables allows for flexible and modular modeling of transaction costs, liquidity costs, and market impact.
• The use of least-squares regression on a discrete grid enables accurate approximation of the backward dynamic programming recursion.
• Local interpolation and adaptive refinement significantly improve the precision of optimal allocation estimates without excessive computational cost.
• The framework achieves polynomial runtime growth with respect to portfolio dimension, ensuring scalability for realistic problems.
• The method is empirically validated on a 12-asset portfolio, demonstrating its viability and robustness in a realistic dynamic allocation setting.