Hidden Markov Model

Robo-Advising in Motion: A Model Predictive Control Approach ArXiv ID: 2601.09127 “View on arXiv” Authors: Tomasz R. Bielecki, Igor Cialenco Abstract Robo-advisors (RAs) are automated portfolio management systems that complement traditional financial advisors by offering lower fees and smaller initial investment requirements. While most existing RAs rely on static, one-period allocation methods, we propose a dynamic, multi-period asset-allocation framework that leverages Model Predictive Control (MPC) to generate suboptimal but practically effective strategies. Our approach combines a Hidden Markov Model with Black-Litterman (BL) methodology to forecast asset returns and covariances, and incorporates practically important constraints, including turnover limits, transaction costs, and target portfolio allocations. We study two predominant optimality criteria in wealth management: dynamic mean-variance (MV) and dynamic risk-budgeting (MRB). Numerical experiments demonstrate that MPC-based strategies consistently outperform myopic approaches, with MV providing flexible and diversified portfolios, while MRB delivers smoother allocations less sensitive to key parameters. These findings highlight the trade-offs between adaptability and stability in practical robo-advising design. ...

High-Frequency Market Manipulation Detection with a Markov-modulated Hawkes process ArXiv ID: 2502.04027 “View on arXiv” Authors: Unknown Abstract This work focuses on a self-exciting point process defined by a Hawkes-like intensity and a switching mechanism based on a hidden Markov chain. Previous works in such a setting assume constant intensities between consecutive events. We extend the model to general Hawkes excitation kernels that are piecewise constant between events. We develop an expectation-maximization algorithm for the statistical inference of the Hawkes intensities parameters as well as the state transition probabilities. The numerical convergence of the estimators is extensively tested on simulated data. Using high-frequency cryptocurrency data on a top centralized exchange, we apply the model to the detection of anomalous bursts of trades. We benchmark the goodness-of-fit of the model with the Markov-modulated Poisson process and demonstrate the relevance of the model in detecting suspicious activities. ...

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. ...

Improving Portfolio Performance Using a Novel Method for Predicting Financial Regimes ArXiv ID: 2310.04536 “View on arXiv” Authors: Unknown Abstract This work extends a previous work in regime detection, which allowed trading positions to be profitably adjusted when a new regime was detected, to ex ante prediction of regimes, leading to substantial performance improvements over the earlier model, over all three asset classes considered (equities, commodities, and foreign exchange), over a test period of four years. The proposed new model is also benchmarked over this same period against a hidden Markov model, the most popular current model for financial regime prediction, and against an appropriate index benchmark for each asset class, in the case of the commodities model having a test period cost-adjusted cumulative return over four times higher than that expected from the index. Notably, the proposed model makes use of a contrarian trading strategy, not uncommon in the financial industry but relatively unexplored in machine learning models. The model also makes use of frequent short positions, something not always desirable to investors due to issues of both financial risk and ethics; however, it is discussed how further work could remove this reliance on shorting and allow the construction of a long-only version of the model. ...

Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results ArXiv ID: 2308.02049 “View on arXiv” Authors: Unknown Abstract This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving randomly over time. The arrival dates are modeled as the jump times of a homogeneous Poisson process. Applying Kalman filter techniques we derive estimates of the hidden drift which are described by the conditional mean and covariance of the drift given the observations. The utility maximization problem is solved with dynamic programming methods. We derive the associated dynamic programming equation and study regularization arguments for a rigorous mathematical justification. ...