{"title":"On optimal tracking portfolio in incomplete markets: The classical control and the reinforcement learning approaches","authors":"Lijun Bo, Yijie Huang, Xiang Yu","doi":"arxiv-2311.14318","DOIUrl":"https://doi.org/arxiv-2311.14318","url":null,"abstract":"This paper studies an infinite horizon optimal tracking portfolio problem\u0000using capital injection in incomplete market models. We consider the benchmark\u0000process modelled by a geometric Brownian motion with zero drift driven by some\u0000unhedgeable risk. The relaxed tracking formulation is adopted where the\u0000portfolio value compensated by the injected capital needs to outperform the\u0000benchmark process at any time, and the goal is to minimize the cost of the\u0000discounted total capital injection. In the first part, we solve the stochastic\u0000control problem when the market model is known, for which the equivalent\u0000auxiliary control problem with reflections and the associated HJB equation with\u0000a Neumann boundary condition are studied. In the second part, the market model\u0000is assumed to be unknown, for which we consider the exploratory formulation of\u0000the control problem with entropy regularizer and develop the continuous-time\u0000q-learning algorithm for the stochastic control problem with state reflections.\u0000In an illustrative example, we show the satisfactory performance of the\u0000q-learning algorithm.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"6 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Curriculum Learning and Imitation Learning for Model-free Control on Financial Time-series","authors":"Woosung Koh, Insu Choi, Yuntae Jang, Gimin Kang, Woo Chang Kim","doi":"arxiv-2311.13326","DOIUrl":"https://doi.org/arxiv-2311.13326","url":null,"abstract":"Curriculum learning and imitation learning have been leveraged extensively in\u0000the robotics domain. However, minimal research has been done on leveraging\u0000these ideas on control tasks over highly stochastic time-series data. Here, we\u0000theoretically and empirically explore these approaches in a representative\u0000control task over complex time-series data. We implement the fundamental ideas\u0000of curriculum learning via data augmentation, while imitation learning is\u0000implemented via policy distillation from an oracle. Our findings reveal that\u0000curriculum learning should be considered a novel direction in improving\u0000control-task performance over complex time-series. Our ample random-seed\u0000out-sample empirics and ablation studies are highly encouraging for curriculum\u0000learning for time-series control. These findings are especially encouraging as\u0000we tune all overlapping hyperparameters on the baseline -- giving an advantage\u0000to the baseline. On the other hand, we find that imitation learning should be\u0000used with caution.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"High order universal portfolios","authors":"Gabriel Turinici","doi":"arxiv-2311.13564","DOIUrl":"https://doi.org/arxiv-2311.13564","url":null,"abstract":"The Cover universal portfolio (UP from now on) has many interesting\u0000theoretical and numerical properties and was investigated for a long time.\u0000Building on it, we explore what happens when we add this UP to the market as a\u0000new synthetic asset and construct by recurrence higher order UPs. We\u0000investigate some important theoretical properties of the high order UPs and\u0000show in particular that they are indeed different from the Cover UP and are\u0000capable to break the time permutation invariance. Numerical experiences on a\u0000benchmark from the literature show that in all cases high order UPs improve\u0000Cover's UP performances.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"6 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michele Azzone, Maria Chiara Pocelli, Davide Stocco
{"title":"Can we hedge carbon risk? A network embedding approach","authors":"Michele Azzone, Maria Chiara Pocelli, Davide Stocco","doi":"arxiv-2311.12450","DOIUrl":"https://doi.org/arxiv-2311.12450","url":null,"abstract":"Sustainable investing refers to the integration of environmental and social\u0000aspects in investors' decisions. We propose a novel methodology based on the\u0000Triangulated Maximally Filtered Graph and node2vec algorithms to construct an\u0000hedging portfolio for climate risk, represented by various risk factors, among\u0000which the CO2 and the ESG ones. The CO2 factor is strongly correlated\u0000consistently over time with the Utility sector, which is the most carbon\u0000intensive in the S&P 500 index. Conversely, identifying a group of sectors\u0000linked to the ESG factor proves challenging. As a consequence, while it is\u0000possible to obtain an efficient hedging portfolio strategy with our methodology\u0000for the carbon factor, the same cannot be achieved for the ESG one. The ESG\u0000scores appears to be an indicator too broadly defined for market applications.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"7 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal Portfolio with Ratio Type Periodic Evaluation under Short-Selling Prohibition","authors":"Wenyuan Wang, Kaixin Yan, Xiang Yu","doi":"arxiv-2311.12517","DOIUrl":"https://doi.org/arxiv-2311.12517","url":null,"abstract":"This paper studies some unconventional utility maximization problems when the\u0000ratio type relative portfolio performance is periodically evaluated over an\u0000infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks.\u0000Our goal is to understand impacts of the short-selling constraint and the\u0000periodic reward structure on the long-run optimal portfolio strategy. Under\u0000logarithmic and power utilities, we first reformulate the original problem into\u0000an auxiliary one-period optimization problem. To cope with the auxiliary\u0000problem with no short-selling, the dual control problem is introduced and\u0000studied, which gives the characterization of the candidate optimal portfolio\u0000within one period. With the help of the obtained results from the auxiliary\u0000problem, the value function and the optimal constrained portfolio for the\u0000original problem with periodic evaluation over an infinite horizon can be\u0000further derived and verified, allowing us to discuss some interesting financial\u0000implications under the new performance paradigm.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"7 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"DeFi Security: Turning The Weakest Link Into The Strongest Attraction","authors":"Ravi Kashyap","doi":"arxiv-2312.00033","DOIUrl":"https://doi.org/arxiv-2312.00033","url":null,"abstract":"The primary innovation we pioneer -- focused on blockchain information\u0000security -- is called the Safe-House. The Safe-House is badly needed since\u0000there are many ongoing hacks and security concerns in the DeFi space right now.\u0000The Safe-House is a piece of engineering sophistication that utilizes existing\u0000blockchain principles to bring about greater security when customer assets are\u0000moved around. The Safe-House logic is easily implemented as smart contracts on\u0000any decentralized system. The amount of funds at risk from both internal and\u0000external parties -- and hence the maximum one time loss -- is guaranteed to\u0000stay within the specified limits based on cryptographic fundamentals. To improve the safety of the Safe-House even further, we adapt the one time\u0000password (OPT) concept to operate using blockchain technology. Well suited to\u0000blockchain cryptographic nuances, our secondary advancement can be termed the\u0000one time next time password (OTNTP) mechanism. The OTNTP is designed to\u0000complement the Safe-House making it even more safe. We provide a detailed threat assessment model -- discussing the risks faced\u0000by DeFi protocols and the specific risks that apply to blockchain fund\u0000management -- and give technical arguments regarding how these threats can be\u0000overcome in a robust manner. We discuss how the Safe-House can participate with\u0000other external yield generation protocols in a secure way. We provide reasons\u0000for why the Safe-House increases safety without sacrificing the efficiency of\u0000operation. We start with a high level intuitive description of the landscape,\u0000the corresponding problems and our solutions. We then supplement this overview\u0000with detailed discussions including the corresponding mathematical formulations\u0000and pointers for technological implementation. This approach ensures that the\u0000article is accessible to a broad audience.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"118 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal Retirement Choice under Age-dependent Force of Mortality","authors":"Giorgio Ferrari, Shihao Zhu","doi":"arxiv-2311.12169","DOIUrl":"https://doi.org/arxiv-2311.12169","url":null,"abstract":"This paper examines the retirement decision, optimal investment, and\u0000consumption strategies under an age-dependent force of mortality. We formulate\u0000the optimization problem as a combined stochastic control and optimal stopping\u0000problem with a random time horizon, featuring three state variables: wealth,\u0000labor income, and force of mortality. To address this problem, we transform it\u0000into its dual form, which is a finite time horizon, three-dimensional\u0000degenerate optimal stopping problem with interconnected dynamics. We establish\u0000the existence of an optimal retirement boundary that splits the state space\u0000into continuation and stopping regions. Regularity of the optimal stopping\u0000value function is derived and the boundary is proved to be Lipschitz\u0000continuous, and it is characterized as the unique solution to a nonlinear\u0000integral equation, which we compute numerically. In the original coordinates,\u0000the agent thus retires whenever her wealth exceeds an age-, labor income- and\u0000mortality-dependent transformed version of the optimal stopping boundary. We\u0000also provide numerical illustrations of the optimal strategies, including the\u0000sensitivities of the optimal retirement boundary concerning the relevant\u0000model's parameters.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"7 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal Transport Divergences induced by Scoring Functions","authors":"Silvana M. Pesenti, Steven Vanduffel","doi":"arxiv-2311.12183","DOIUrl":"https://doi.org/arxiv-2311.12183","url":null,"abstract":"We employ scoring functions, used in statistics for eliciting risk\u0000functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport\u0000problem. This gives raise to a rich variety of novel asymmetric MK divergences,\u0000which subsume the family of Bregman-Wasserstein divergences. We show that for\u0000distributions on the real line, the comonotonic coupling is optimal for the\u0000majority the new divergences. Specifically, we derive the optimal coupling of\u0000the MK divergences induced by functionals including the mean, generalised\u0000quantiles, expectiles, and shortfall measures. Furthermore, we show that while\u0000any elicitable law-invariant convex risk measure gives raise to infinitely many\u0000MK divergences, the comonotonic coupling is simultaneously optimal. The novel MK divergences, which can be efficiently calculated, open an array\u0000of applications in robust stochastic optimisation. We derive sharp bounds on\u0000distortion risk measures under a Bregman-Wasserstein divergence constraint, and\u0000solve for cost-efficient portfolio strategies under benchmark constraints.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"7 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sector Rotation by Factor Model and Fundamental Analysis","authors":"Runjia Yang, Beining Shi","doi":"arxiv-2401.00001","DOIUrl":"https://doi.org/arxiv-2401.00001","url":null,"abstract":"This study presents an analytical approach to sector rotation, leveraging\u0000both factor models and fundamental metrics. We initiate with a systematic\u0000classification of sectors, followed by an empirical investigation into their\u0000returns. Through factor analysis, the paper underscores the significance of\u0000momentum and short-term reversion in dictating sectoral shifts. A subsequent\u0000in-depth fundamental analysis evaluates metrics such as PE, PB, EV-to-EBITDA,\u0000Dividend Yield, among others. Our primary contribution lies in developing a\u0000predictive framework based on these fundamental indicators. The constructed\u0000models, post rigorous training, exhibit noteworthy predictive capabilities. The\u0000findings furnish a nuanced understanding of sector rotation strategies, with\u0000implications for asset management and portfolio construction in the financial\u0000domain.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"244 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139079880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wentao Zhang, Yilei Zhao, Shuo Sun, Jie Ying, Yonggang Xie, Zitao Song, Xinrun Wang, Bo An
{"title":"Reinforcement Learning with Maskable Stock Representation for Portfolio Management in Customizable Stock Pools","authors":"Wentao Zhang, Yilei Zhao, Shuo Sun, Jie Ying, Yonggang Xie, Zitao Song, Xinrun Wang, Bo An","doi":"arxiv-2311.10801","DOIUrl":"https://doi.org/arxiv-2311.10801","url":null,"abstract":"Portfolio management (PM) is a fundamental financial trading task, which\u0000explores the optimal periodical reallocation of capitals into different stocks\u0000to pursue long-term profits. Reinforcement learning (RL) has recently shown its\u0000potential to train profitable agents for PM through interacting with financial\u0000markets. However, existing work mostly focuses on fixed stock pools, which is\u0000inconsistent with investors' practical demand. Specifically, the target stock\u0000pool of different investors varies dramatically due to their discrepancy on\u0000market states and individual investors may temporally adjust stocks they desire\u0000to trade (e.g., adding one popular stocks), which lead to customizable stock\u0000pools (CSPs). Existing RL methods require to retrain RL agents even with a tiny\u0000change of the stock pool, which leads to high computational cost and unstable\u0000performance. To tackle this challenge, we propose EarnMore, a rEinforcement\u0000leARNing framework with Maskable stOck REpresentation to handle PM with CSPs\u0000through one-shot training in a global stock pool (GSP). Specifically, we first\u0000introduce a mechanism to mask out the representation of the stocks outside the\u0000target pool. Second, we learn meaningful stock representations through a\u0000self-supervised masking and reconstruction process. Third, a re-weighting\u0000mechanism is designed to make the portfolio concentrate on favorable stocks and\u0000neglect the stocks outside the target pool. Through extensive experiments on 8\u0000subset stock pools of the US stock market, we demonstrate that EarnMore\u0000significantly outperforms 14 state-of-the-art baselines in terms of 6 popular\u0000financial metrics with over 40% improvement on profit.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"7 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}