[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118945-en":3,"doc-seo-118945-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118945,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Generative Machine Learning for Multivariate Equity Returns - Abstract","Generative Machine Learning for Multivariate Equity Returns研究如何用深度生成模型学习股票收益的联合分布，以支持风险预测与资产配置决策。文中比较了条件重要性加权自编码器（CIWAE，可视为变分自编码器变体）与条件归一化流，用于在高维情形下建模接近500维的S&P 500联合分布。作者展示该生成模型可用于生成逼真合成数据、估计波动率与相关性、开展风险分析（如VaR）以及提升投资组合优化表现。","Generative Machine Learning for Multivariate Equity Returns  \nRuslan Tepelyan∗ Bloomberg New York, USA[rtepelyan@bloomberg.net](rtepelyan@bloomberg.net)  \nAchintya Gopal∗ Bloomberg New York, USA [agopal6@bloomberg.net](agopal6@bloomberg.net)  \narXiv :2311 . 14735v1 [ q-fin . ST] 21 Nov 2023  \nABSTRACT  \nThe use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the underlying data, similar to the classical methods common in finance of fitting statistical models to data. In this work, we explore the efficacy of using modern machine learning methods, specifically conditional importance weighted autoencoders (a variant of variational autoencoders) and conditional normalizing flows, for the task of modeling the returns of equities. The main problem we work to address is modeling the joint distribution of all the members of the S&P 500, or, in other words, learning a 500-dimensional joint distribution. We show that this generative model has a broad range of applications in finance, including generating realistic synthetic data, volatility and correlation estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization.  \nCCS CONCEPTS  \n• Applied computing; • Computing methodologies → Machine learning; • Mathematics of computing → Probability and statistics;  \nKEYWORDS  \nStock Returns, Generative Modeling, Variational Autoencoders, Normalizing Flows, Risk Forecasting, Portfolio Optimization  \n1 INTRODUCTION  \nRisk forecasting is an important problem in finance to help estimate portfolio risk, volatility, and correlation, as well as being an input for portfolio optimization. These problems are often solved via statistical quantities such as quantiles (for VaR), standard deviation (for volatility), Pearson correlations, etc. One approach is to derive an estimator specific to the statistical quantity (e.g., [10, 18]); another approach is to develop a statistical model such as GARCH [8] or multivariate GARCH [7] that learns the distribution of returns, after which any statistical quantity can be queried from the learned distribution. In this work, we focus on a deep learning approach to developing a statistical model that learns the multivariate distribution of stock returns.  \nThe generative models of deep learning are also just statistical models; examples include variational autoencoders (VAEs,[16]), normalizing flows [4, 23], autoregressive models as used in large language models [22, 25], etc. Given this, we ask the question,“can we use deep probabilistic models for the task of modeling distributions of returns?” Phrased another way, the problem is: given all of the data up to a particular point in time, can we model  \n∗ Both authors contributed equally to this research.  \nthe return of a stock over the next day as an arbitrary probability distribution? Modern deep learning techniques allow us to fit such distributions, and as long as these distributions are well-calibrated, we can rely, in a statistical sense, on any downstream results derived from them.  \nPrior work has applied deep learning approaches to model single financial time series (e.g., [2, 26]); Wiese et al. [27] applied their approach to modeling two assets by modeling each independently first and then correlating them. However, to our knowledge, no prior work has constructed a method to model the joint distribution of an arbitrary number of stocks; without modeling the joint distribution, the generative model cannot capture the correlations between stock returns. While previous deep learning work has modeled high-dimensional data (e.g., [20, 22]), these methods do not handle a variable number of dimensions, something that is required in modeling stocks, since stocks can be added and removed from the universe (i.e., a varying number of dimensions at each time ste","cbCaisltheqIrsgR","https://ap.wps.com/l/cbCaisltheqIrsgR","pdf",1219846,1,13,"English","en",105,"# Introduction\n## Risk forecasting and statistical vs deep models\n## Proposed conditional generative approach\n# Background\n## Conditional distributions and likelihood computation","[{\"question\":\"本文要解决的核心问题是什么？\",\"answer\":\"如何使用深度概率生成模型建模多只股票收益的联合分布，从而刻画相关性并服务下游风险预测与组合优化任务。\"},{\"question\":\"作者使用了哪些生成模型来进行建模？\",\"answer\":\"采用条件重要性加权自编码器（CIWAE，用于因子建模）以及条件归一化流（用于单只股票收益建模），并在采样时使用自回归方式。\"},{\"question\":\"该方法的主要应用和效果体现在哪里？\",\"answer\":\"用于生成逼真的合成数据、估计波动率与相关性、进行风险分析（如组合的VaR），并在单变量与多变量场景、以及组合优于市场的表现上展示有效性。\"}]","Generative Machine Learning for Multivariate Equity Returns - Abstract | PDF",1785721137,33,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"generative-machine-learning-for-multivariate-equity-returns-abstract","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/generative-machine-learning-for-multivariate-equity-returns-abstract/118945/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-03",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"本文要解决的核心问题是什么？","Question",{"text":76,"@type":77},"如何使用深度概率生成模型建模多只股票收益的联合分布，从而刻画相关性并服务下游风险预测与组合优化任务。","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"作者使用了哪些生成模型来进行建模？",{"text":81,"@type":77},"采用条件重要性加权自编码器（CIWAE，用于因子建模）以及条件归一化流（用于单只股票收益建模），并在采样时使用自回归方式。",{"name":83,"@type":74,"acceptedAnswer":84},"该方法的主要应用和效果体现在哪里？",{"text":85,"@type":77},"用于生成逼真的合成数据、估计波动率与相关性、进行风险分析（如组合的VaR），并在单变量与多变量场景、以及组合优于市场的表现上展示有效性。","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]