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1. Efficient and Near-Optimal Online Portfolio Selection

   Jézéquel, R; Ostrovskii, D.; Gaillard, P. (October 2022, ArXivorg)

   In the problem of online portfolio selection as formulated by Cover (1991), the trader repeatedly distributes her capital over d assets in each of T>1 rounds, with the goal of maximizing the total return. Cover proposed an algorithm, termed Universal Portfolios, that performs nearly as well as the best (in hindsight) static assignment of a portfolio, with an O(dlog(T)) regret in terms of the logarithmic return. Without imposing any restrictions on the market this guarantee is known to be worst-case optimal, and no other algorithm attaining it has been discovered so far. Unfortunately, Cover's algorithm crucially relies on computing certain d-dimensional integral which must be approximated in any implementation; this results in a prohibitive O(d^4(T+d)^14) per-round runtime for the fastest known implementation due to Kalai and Vempala (2002). We propose an algorithm for online portfolio selection that admits essentially the same regret guarantee as Universal Portfolios -- up to a constant factor and replacement of log(T) with log(T+d) -- yet has a drastically reduced runtime of O(d^(T+d)) per round. The selected portfolio minimizes the current logarithmic loss regularized by the log-determinant of its Hessian -- equivalently, the hybrid logarithmic-volumetric barrier of the polytope specified by the asset return vectors. As such, our work reveals surprising connections of online portfolio selection with two classical topics in optimization theory: cutting-plane and interior-point algorithms. 

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2. TIME-INCONSISTENT MARKOVIAN CONTROL PROBLEMS UNDER MODEL UNCERTAINTY WITH APPLICATION TO THE MEAN-VARIANCE PORTFOLIO SELECTION

   https://doi.org/10.1142/S0219024921500035  

   BIELECKI, TOMASZ R.; CHEN, TAO; CIALENCO, IGOR (February 2021, International Journal of Theoretical and Applied Finance)

   null (Ed.)

   In this paper, we study a class of time-inconsistent terminal Markovian control problems in discrete time subject to model uncertainty. We combine the concept of the sub-game perfect strategies with the adaptive robust stochastic control method to tackle the theoretical aspects of the considered stochastic control problem. Consequently, as an important application of the theoretical results and by applying a machine learning algorithm we solve numerically the mean-variance portfolio selection problem under the model uncertainty. 

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3. Symphony in the Latent Space: Provably Integrating High-dimensional Techniques with Non-linear Machine Learning Models

   https://doi.org/10.1609/aaai.v37i9.26233  

   Wu, Qiong; Li, Jian; Liu, Zhenming; Li, Yanhua; Cucuringu, Mihai (February 2023, AAAI)

   This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to forecast the future evolution of ensembles of multivariate time series in such applications (e.g., the future return of a financial asset or the future popularity of a Twitter account). Designing ML algorithms for such systems requires addressing the challenges of high-dimensional interactions and non-linearity. Existing approaches usually adopt an ad-hoc approach to integrating high-dimensional techniques into non-linear models and re- cent studies have shown these approaches have questionable efficacy in time-evolving interacting systems. To this end, we propose a novel framework, which we dub as the additive influence model. Under our modeling assump- tion, we show that it is possible to decouple the learning of high-dimensional interactions from the learning of non-linear feature interactions. To learn the high-dimensional interac- tions, we leverage kernel-based techniques, with provable guarantees, to embed the entities in a low-dimensional latent space. To learn the non-linear feature-response interactions, we generalize prominent machine learning techniques, includ- ing designing a new statistically sound non-parametric method and an ensemble learning algorithm optimized for vector re- gressions. Extensive experiments on two common applica- tions demonstrate that our new algorithms deliver significantly stronger forecasting power compared to standard and recently proposed methods. 

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4. Symphony in the Latent Space: Provably Integrating High-dimensional Techniques with Non-linear Machine Learning Models

   Qiong Wu; Jian Li; Zhenming Liu; Yanhua Li; Mihai Cucuringu (April 2023, Proceedings of the AAAI Conference on Artificial Intelligence)

   This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interac- tions between users in a social network. Our goal is to forecast the future evolution of ensembles of multivariate time series in such applications (e.g., the future return of a financial asset or the future popularity of a Twitter account). Designing ML algorithms for such systems requires addressing the challenges of high-dimensional interactions and non-linearity. Existing approaches usually adopt an ad-hoc approach to integrating high-dimensional techniques into non-linear models and re- cent studies have shown these approaches have questionable efficacy in time-evolving interacting systems. To this end, we propose a novel framework, which we dub as the additive influence model. Under our modeling assump- tion, we show that it is possible to decouple the learning of high-dimensional interactions from the learning of non-linear feature interactions. To learn the high-dimensional interac- tions, we leverage kernel-based techniques, with provable guarantees, to embed the entities in a low-dimensional latent space. To learn the non-linear feature-response interactions, we generalize prominent machine learning techniques, includ- ing designing a new statistically sound non-parametric method and an ensemble learning algorithm optimized for vector re- gressions. Extensive experiments on two common applica- tions demonstrate that our new algorithms deliver significantly stronger forecasting power compared to standard and recently proposed methods. 

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5. Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

   Blanchet, Jose; Chen, Lin; Zhou, Xunyu. (January 2020, Management science)

   We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. 

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