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A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization with MGARCH and Small Transaction Costs
- Publication Year :
- 2023
-
Abstract
- 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 $\epsilon>0$ that controls the magnitude of transaction costs. When $\epsilon$ is small, we can implement an NN algorithm based on the expansion of the solution in powers of $\epsilon$. 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.
- Subjects :
- Quantitative Finance - Computational Finance
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2301.10869
- Document Type :
- Working Paper