Ensembling Portfolio Strategies for Long-Term Investments: A Distribution-Free Preference Framework for Decision-Making and Algorithms ArXiv ID: 2406.03652 “View on arXiv” Authors: Unknown Abstract This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies’ performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor’s preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance. ...

Filtered not Mixed: Stochastic Filtering-Based Online Gating for Mixture of Large Language Models ArXiv ID: 2406.02969 “View on arXiv” Authors: Unknown Abstract We propose MoE-F - a formalized mechanism for combining $N$ pre-trained Large Language Models (LLMs) for online time-series prediction by adaptively forecasting the best weighting of LLM predictions at every time step. Our mechanism leverages the conditional information in each expert’s running performance to forecast the best combination of LLMs for predicting the time series in its next step. Diverging from static (learned) Mixture of Experts (MoE) methods, our approach employs time-adaptive stochastic filtering techniques to combine experts. By framing the expert selection problem as a finite state-space, continuous-time Hidden Markov model (HMM), we can leverage the Wohman-Shiryaev filter. Our approach first constructs N parallel filters corresponding to each of the $N$ individual LLMs. Each filter proposes its best combination of LLMs, given the information that they have access to. Subsequently, the N filter outputs are optimally aggregated to maximize their robust predictive power, and this update is computed efficiently via a closed-form expression, generating our ensemble predictor. Our contributions are: (I) the MoE-F plug-and-play filtering harness algorithm, (II) theoretical optimality guarantees of the proposed filtering-based gating algorithm (via optimality guarantees for its parallel Bayesian filtering and its robust aggregation steps), and (III) empirical evaluation and ablative results using state-of-the-art foundational and MoE LLMs on a real-world Financial Market Movement task where MoE-F attains a remarkable 17% absolute and 48.5% relative F1 measure improvement over the next best performing individual LLM expert predicting short-horizon market movement based on streaming news. Further, we provide empirical evidence of substantial performance gains in applying MoE-F over specialized models in the long-horizon time-series forecasting domain. ...

Mean field equilibrium asset pricing model with habit formation ArXiv ID: 2406.02155 “View on arXiv” Authors: Unknown Abstract This paper presents an asset pricing model in an incomplete market involving a large number of heterogeneous agents based on the mean field game theory. In the model, we incorporate habit formation in consumption preferences, which has been widely used to explain various phenomena in financial economics. In order to characterize the market-clearing equilibrium, we derive a quadratic-growth mean field backward stochastic differential equation (BSDE) and study its well-posedness and asymptotic behavior in the large population limit. Additionally, we introduce an exponential quadratic Gaussian reformulation of the asset pricing model, in which the solution is obtained in a semi-analytic form. ...

Pricing and calibration in the 4-factor path-dependent volatility model ArXiv ID: 2406.02319 “View on arXiv” Authors: Unknown Abstract We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns. We discuss the influence of an additional parameter that unlocks enough volatility on the upside to reproduce the implied volatility smiles of S&P 500 and VIX options. This PDV model, motivated by empirical studies, comes with computational challenges, especially in relation to VIX options pricing and calibration. We propose an accurate \emph{“pathwise”} neural network approximation of the VIX which leverages on the Markovianity of the 4-factor version of the model. The VIX is learned pathwise as a function of the Markovian factors and the model parameters. We use this approximation to tackle the joint calibration of S&P 500 and VIX options, quickly sample VIX paths, and price derivatives that jointly depend on S&P 500 and VIX. As an interesting aside, we also show that this \emph{“time-homogeneous”}, low-parametric, Markovian PDV model is able to fit the whole surface of S&P 500 implied volatilities remarkably well. ...

Simulation-based approach for Multiproject Scheduling based on composite priority rules ArXiv ID: 2406.02102 “View on arXiv” Authors: Unknown Abstract This paper presents a simulation approach to enhance the performance of heuristics for multi-project scheduling. Unlike other heuristics available in the literature that use only one priority criterion for resource allocation, this paper proposes a structured way to sequentially apply more than one priority criterion for this purpose. By means of simulation, different feasible schedules are obtained to, therefore, increase the probability of finding the schedule with the shortest duration. The performance of this simulation approach was validated with the MPSPLib library, one of the most prominent libraries for resource-constrained multi-project scheduling. These results highlight the proposed method as a useful option for addressing limited time and resources in portfolio management. ...

Temporal distribution of clusters of investors and their application in prediction with expert advice ArXiv ID: 2406.19403 “View on arXiv” Authors: Unknown Abstract Financial organisations such as brokers face a significant challenge in servicing the investment needs of thousands of their traders worldwide. This task is further compounded since individual traders will have their own risk appetite and investment goals. Traders may look to capture short-term trends in the market which last only seconds to minutes, or they may have longer-term views which last several days to months. To reduce the complexity of this task, client trades can be clustered. By examining such clusters, we would likely observe many traders following common patterns of investment, but how do these patterns vary through time? Knowledge regarding the temporal distributions of such clusters may help financial institutions manage the overall portfolio of risk that accumulates from underlying trader positions. This study contributes to the field by demonstrating that the distribution of clusters derived from the real-world trades of 20k Foreign Exchange (FX) traders (from 2015 to 2017) is described in accordance with Ewens’ Sampling Distribution. Further, we show that the Aggregating Algorithm (AA), an on-line prediction with expert advice algorithm, can be applied to the aforementioned real-world data in order to improve the returns of portfolios of trader risk. However we found that the AA ‘struggles’ when presented with too many trader ``experts’’, especially when there are many trades with similar overall patterns. To help overcome this challenge, we have applied and compared the use of Statistically Validated Networks (SVN) with a hierarchical clustering approach on a subset of the data, demonstrating that both approaches can be used to significantly improve results of the AA in terms of profitability and smoothness of returns. ...

A Geometric Approach To Asset Allocation With Investor Views ArXiv ID: 2406.01199 “View on arXiv” Authors: Unknown Abstract In this article, a geometric approach to incorporating investor views in portfolio construction is presented. In particular, the proposed approach utilizes the notion of generalized Wasserstein barycenter (GWB) to combine the statistical information about asset returns with investor views to obtain an updated estimate of the asset drifts and covariance, which are then fed into a mean-variance optimizer as inputs. Quantitative comparisons of the proposed geometric approach with the conventional Black-Litterman model (and a closely related variant) are presented. The proposed geometric approach provides investors with more flexibility in specifying their confidence in their views than conventional Black-Litterman model-based approaches. The geometric approach also rewards the investors more for making correct decisions than conventional BL based approaches. We provide empirical and theoretical justifications for our claim. ...

MOT: A Mixture of Actors Reinforcement Learning Method by Optimal Transport for Algorithmic Trading ArXiv ID: 2407.01577 “View on arXiv” Authors: Unknown Abstract Algorithmic trading refers to executing buy and sell orders for specific assets based on automatically identified trading opportunities. Strategies based on reinforcement learning (RL) have demonstrated remarkable capabilities in addressing algorithmic trading problems. However, the trading patterns differ among market conditions due to shifted distribution data. Ignoring multiple patterns in the data will undermine the performance of RL. In this paper, we propose MOT,which designs multiple actors with disentangled representation learning to model the different patterns of the market. Furthermore, we incorporate the Optimal Transport (OT) algorithm to allocate samples to the appropriate actor by introducing a regularization loss term. Additionally, we propose Pretrain Module to facilitate imitation learning by aligning the outputs of actors with expert strategy and better balance the exploration and exploitation of RL. Experimental results on real futures market data demonstrate that MOT exhibits excellent profit capabilities while balancing risks. Ablation studies validate the effectiveness of the components of MOT. ...

Statistics-Informed Parameterized Quantum Circuit via Maximum Entropy Principle for Data Science and Finance ArXiv ID: 2406.01335 “View on arXiv” Authors: Unknown Abstract Quantum machine learning has demonstrated significant potential in solving practical problems, particularly in statistics-focused areas such as data science and finance. However, challenges remain in preparing and learning statistical models on a quantum processor due to issues with trainability and interpretability. In this letter, we utilize the maximum entropy principle to design a statistics-informed parameterized quantum circuit (SI-PQC) for efficiently preparing and training of quantum computational statistical models, including arbitrary distributions and their weighted mixtures. The SI-PQC features a static structure with trainable parameters, enabling in-depth optimized circuit compilation, exponential reductions in resource and time consumption, and improved trainability and interpretability for learning quantum states and classical model parameters simultaneously. As an efficient subroutine for preparing and learning in various quantum algorithms, the SI-PQC addresses the input bottleneck and facilitates the injection of prior knowledge. ...

Gated recurrent neural network with TPE Bayesian optimization for enhancing stock index prediction accuracy ArXiv ID: 2406.02604 “View on arXiv” Authors: Unknown Abstract The recent advancement of deep learning architectures, neural networks, and the combination of abundant financial data and powerful computers are transforming finance, leading us to develop an advanced method for predicting future stock prices. However, the accessibility of investment and trading at everyone’s fingertips made the stock markets increasingly intricate and prone to volatility. The increased complexity and volatility of the stock market have driven demand for more models, which would effectively capture high volatility and non-linear behavior of the different stock prices. This study explored gated recurrent neural network (GRNN) algorithms such as LSTM (long short-term memory), GRU (gated recurrent unit), and hybrid models like GRU-LSTM, LSTM-GRU, with Tree-structured Parzen Estimator (TPE) Bayesian optimization for hyperparameter optimization (TPE-GRNN). The aim is to improve the prediction accuracy of the next day’s closing price of the NIFTY 50 index, a prominent Indian stock market index, using TPE-GRNN. A combination of eight influential factors is carefully chosen from fundamental stock data, technical indicators, crude oil price, and macroeconomic data to train the models for capturing the changes in the price of the index with the factors of the broader economy. Single-layer and multi-layer TPE-GRNN models have been developed. The models’ performance is evaluated using standard matrices like R2, MAPE, and RMSE. The analysis of models’ performance reveals the impact of feature selection and hyperparameter optimization (HPO) in enhancing stock index price prediction accuracy. The results show that the MAPE of our proposed TPE-LSTM method is the lowest (best) with respect to all the previous models for stock index price prediction. ...