A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization With MGARCH and Small Transaction Costs
A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization With MGARCH and Small Transaction Costs
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DOI：
10.1109/access.2023.3245570
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发表时间：
2023-01
期刊：
影响因子：
3.9
通讯作者：
A. Papanicolaou;Hao Fu;P. Krishnamurthy;F. Khorrami
中科院分区：
文献类型：
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作者：
A. Papanicolaou;Hao Fu;P. Krishnamurthy;F. Khorrami
我们分析了强化学习（RL）的最佳投资组合的均值-方差偏好的设置多变量广义自回归条件异方差（MGRESTIVE）的固定点算法，交易的一个小的惩罚。在递归RL循环内使用神经网络（NN）架构获得数值解。一个不动点定理证明了神经网络的逼近误差有一个big-oh界，我们可以通过增加神经网络参数的数量来减少。交易惩罚的函数形式有一个控制交易成本大小的参数$\n>0$。当$\n $很小时，我们可以实现一个NN算法的基础上扩展的解决方案的权力$\n $。这种扩展有一个基本项等于近视的解决方案与明确的形式，和一阶校正项，我们计算的RL循环。我们的基于扩展的算法是稳定的，允许快速计算，并输出一个解决方案，显示积极的测试性能。
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.