TY - JOUR

T1 - A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization With MGARCH and Small Transaction Costs

AU - Papanicolaou, Andrew

AU - Fu, Hao

AU - Krishnamurthy, Prashanth

AU - Khorrami, Farshad

N1 - Funding Information:
This work was supported in part by NSF grant DMS-1907518 and in part by the New York University Abu Dhabi (NYUAD) Center for Artificial Intelligence and Robotics, funded by Tamkeen under the NYUAD Research Institute Award CG010.
Publisher Copyright:
© 2013 IEEE.

PY - 2023

Y1 - 2023

N2 - We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter ϵ >0 that controls the magnitude of transaction costs. When ϵ is small, we can implement an NN algorithm based on the expansion of the solution in powers of ϵ. This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance.

AB - We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter ϵ >0 that controls the magnitude of transaction costs. When ϵ is small, we can implement an NN algorithm based on the expansion of the solution in powers of ϵ. This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance.

KW - Hetereoskedasticity

KW - MGARCH

KW - deep neural networks

KW - fixed-point algorithms

KW - reinforcement learning

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U2 - 10.1109/ACCESS.2023.3245570

DO - 10.1109/ACCESS.2023.3245570

M3 - Article

AN - SCOPUS:85149182551

SN - 2169-3536

VL - 11

SP - 16774

EP - 16792

JO - IEEE Access

JF - IEEE Access

ER -