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

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