## 1 Introduction
[13] conditioned on a time series of recent returns, and [PERSON] [14] conditioned on current VIX levels and also on a time series of a 'principal' asset returns for generating multivariate FTS data for multiple assets. However, none of these approaches directly address the empirical issue of regime imbalance in the training data. [PERSON] et al. [15] partially addressed this by selecting a balanced time period between 2007 and 2011 based on heuristical domain knowledge but did not utilise a larger volume of data available for learning. [PERSON] et al. [13] conditioned on the most recent 252 trading days (1 year) of recent historical returns using training data between 2001 and 2013 to generate 1260 days (5 years) of data to assess the training strategy performance. [PERSON] [14] used 100 days of historical S&P500 data as a conditioning variable between 2004 and 2015 to generate joint S&P500 and VIX data. To address regime imbalance and learning a generative model specific to a particular historical regime, we propose a novel approach called a regime-specific Quant GAN (RSQGAN). RSQGAN is a conditional GAN [18] for FTS that extends the Quant GAN (QGAN) model [12] demonstrated for modelling unconditional FTS data. In addition, the aforementioned cGAN studies for FTS data used GAN quality evaluation measures tailored for specific commercial applications: (1) the fine-tuning of trading strategies and/or data augmentation for training trading strategies to maximise risk-adjusted returns [13]; (2) value at risk and expected shortfall estimation [15]; and (3) implicit evidence that cGAN-generated synthetic data augments training data sets and improves the out-of-sample discriminator performance [14; 19]. To directly assess synthetic data quality, particularly for 'crisis' regimes, a number of key evaluation criteria are proposed to assess the improvement in the quality of capturing path-dependent time series behaviour in these regimes so they might be acted on in real-world risk management contexts. The contributions of this paper to existing FTS GAN approaches are threefold:  
1. The use of a structural breakpoint algorithm, greedy Gaussian segmentation [20], to learn time-dependent class categories ('regimes') to be used as embedding conditions and cluster time series data in pre-processing to train the conditional RSQGAN;
2. A user-controlled hyper-parameter method in RSQGAN topological design ('\(z\)-_clipping_') as originally proposed by [PERSON] et al. [21] in BigGAN, which enables users to directly control the variability of synthetic data outputs; and
3. An empirical evaluation of the selection of GAN performance metrics for specifically evaluating synthetic FTS data quality for rarer crisis regimes. This paper demonstrates that RSQGAN is able to achieve improvements across multiple quality evaluation metrics for synthetic crisis regime data, relative to an unconditional QGAN [12] model using the same topology but exclusively trained on crisis regime data. This suggests that the RSQGAN model can learn a useful crisis regime embedding representation and benefits from parameter sharing by learning useful time series features from the behaviour of majority (non-crisis) regime classes. The rest of this paper is structured as follows. In Section 2, we give a high-level overview of GANs and key issues encountered in training. In Section 3, highlights are (i) an overview of the GAN research literature and (ii) innovations in image GAN architecture relevant to developing the RSQGAN architecture. In Section 4, an overview is provided of research papers demonstrating the application of GANs to the FTS data domain. In Section 5, the structural breakpoint algorithm, greedy Gaussian segmentation (GGS) [20], for segmenting time series into regimes for class encoding is briefly described. A description of the RSQGAN model, which evolved from the QGAN model [12] and its training procedure, is described. The section concludes with an outline of data and experimental methodologies.