2023/01/25 by Andrew C. Papanicolaou, Papanicolaou, Andrew, Hao Fu +5
Decision Sciences · Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Markets and Investment Strategies #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2301.10869
openalex publication_date 2023/01/25 · openalex created_date 2023/01/28 · openalex updated_date 2026/07/28
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.