Intra-day price variations in financial markets are driven by the sequence of
orders, called the order flow, that is submitted at high frequency by traders.
This paper introduces a novel application of the Sequence Generative
Adversarial Networks framework to model the order flow, such that random
sequences of the order flow can then be generated to simulate the intra-day
variation of prices. As a benchmark, a well-known parametric model from the
quantitative finance literature is selected. The models are fitted, and then
multiple random paths of the order flow sequences are sampled from each model.
Model performances are then evaluated by using the generated sequences to
simulate price variations, and we compare the empirical regularities between
the price variations produced by the generated and real sequences. The
empirical regularities considered include the distribution of the price
log-returns, the price volatility, and the heavy-tail of the log-returns
distributions. The results show that the order sequences from the generative
model are better able to reproduce the statistical behaviour of real price
variations than the sequences from the benchmark.

使用序列生成对抗网络框架模拟订单流，以生成随机序列来模拟股价波动，通过比较模拟出的股价波动与实际股价波动的经验规律，结果表明生成模型更能够复制真实股价波动的统计行为。

基于生成对抗模型的订单流量的日内价格模拟

Intra-Day Price Simulation with Generative Adversarial Modelling of the  Order Flow

We propose an application of sequence generative adversarial networks
(SeqGAN), which are generative adversarial networks for discrete sequence
generation, for creating polyphonic musical sequences. Instead of a monophonic
melody generation suggested in the original work, we present an efficient
representation of a polyphony MIDI file that simultaneously captures chords and
melodies with dynamic timings. The proposed method condenses duration, octaves,
and keys of both melodies and chords into a single word vector representation,
and recurrent neural networks learn to predict distributions of sequences from
the embedded musical word space. We experiment with the original method and the
least squares method to the discriminator, which is known to stabilize the
training of GANs. The network can create sequences that are musically coherent
and shows an improved quantitative and qualitative measures. We also report
that careful optimization of reinforcement learning signals of the model is
crucial for general application of the model.

本文提出了一种基于序列生成对抗网络的应用方法 (SeqGAN)，用于创建和捕获音符和和弦的多声部音乐序列的表征，同时利用神经网络从该嵌入式音乐词空间的模拟分布中学习预测序列的分布，实验表明该方法可以稳定地训练 GAN 并创造出具有音乐连贯性且在定量和定性方面均有所提升的音乐序列。