arXiv subjects

Jose M. Amigo

Publications and source records attributed to Jose M. Amigo.

5 recordsLinked to original sources

arXiv2026

An Entropy-based Framework for Hybrid Coalitions in Game Theory. Part I: Human Arbitration

Classical Game Theory underpins much of AI and multiagent research, but hybrid Human AI systems require a framework in which execution authority can alternate within a digital environment. We introduce NeoGame Theory, an extension of classical Game Theory for hybrid Human AI coalitions operating under Virtual Nature, the algorithmic analogue of classical (physical) Nature. The framework combines a lexicographic coalition utility with a delegation rule based on the Jensen-Shannon divergence between Human and AI policies. Two thresholds define agreement, contextual, and disagreement regions. In the contextual region, execution follows a scenario specific rule. Apart from the theory, in this paper we develop the first regime, Human arbitration, in which the AI learns by observation and frequency matching while the Human retains final execution authority. We establish the axiomatic basis of the framework and characterize a frequency convergence equilibrium, providing the foundation for later extensions and computational validation.

cs.GT↗

arXiv2025

Enhancing Forex Forecasting Accuracy: The Impact of Hybrid Variable Sets in Cognitive Algorithmic Trading Systems

This paper presents the implementation of an advanced artificial intelligence-based algorithmic trading system specifically designed for the EUR-USD pair within the high-frequency environment of the Forex market. The methodological approach centers on integrating a holistic set of input features: key fundamental macroeconomic variables (for example, Gross Domestic Product and Unemployment Rate) collected from both the Euro Zone and the United States, alongside a comprehensive suite of technical variables (including indicators, oscillators, Fibonacci levels, and price divergences). The performance of the resulting algorithm is evaluated using standard machine learning metrics to quantify predictive accuracy and backtesting simulations across historical data to assess trading profitability and risk. The study concludes with a comparative analysis to determine which class of input features, fundamental or technical, provides greater and more reliable predictive capacity for generating profitable trading signals.

cs.AI↗

arXiv2025

Integration of LSTM Networks in Random Forest Algorithms for Stock Market Trading Predictions

The aim of this paper is the analysis and selection of stock trading systems that combine different models with data of different nature, such as financial and microeconomic information. Specifically, based on previous work by the authors and applying advanced techniques of Machine Learning and Deep Learning, our objective is to formulate trading algorithms for the stock market with empirically tested statistical advantages, thus improving results published in the literature. Our approach integrates Long Short-Term Memory (LSTM) networks with algorithms based on decision trees, such as Random Forest and Gradient Boosting. While the former analyze price patterns of financial assets, the latter are fed with economic data of companies. Numerical simulations of algorithmic trading with data from international companies and 10-weekday predictions confirm that an approach based on both fundamental and technical variables can outperform the usual approaches, which do not combine those two types of variables. In doing so, Random Forest turned out to be the best performer among the decision trees. We also discuss how the prediction performance of such a hybrid approach can be boosted by selecting the technical variables.

q-fin.CP↗

arXiv2013

A closed formula for the topological entropy of multimodal maps based on min-max symbols

Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with conceptually simple models. In the first part of this paper an analytical formula for the topological entropy of twice differentiable multimodal maps is derived, and some basic properties are studied. This expression involves the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore, its proof leads to a numerical algorithm that simplifies a previous one also based on min-max symbols. In the second part of the paper this new algorithm is used to compute the topological entropy of different modal maps. Moreover, it compares favorably to the previous algorithm when computing the topological entropy of the bi- and tri-modal maps considered in the numerical simulations.

math.DS↗

arXiv2005

The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems

Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy rates--measures of new disorder per new observed value--are equal for ergodic finite-alphabet information sources (discrete-time stationary stochastic processes). With this result, we then prove that the same holds for deterministic dynamical systems defined by ergodic maps on $n$% -dimensional intervals. This result generalizes a previous one for piecewise monotone interval maps on the real line (Bandt, Keller and Pompe, "Entropy of interval maps via permutations",\textit{Nonlinearity} \textbf{15}, 1595-602, (2002)), at the expense of requiring ergodicity and using a definition of permutation entropy rate differing in the order of two limits. The case of non-ergodic finite-alphabet sources is also studied and an inequality developed. Finally, the equality of permutation and metric entropy rates is extended to ergodic non-discrete information sources when entropy is replaced by differential entropy in the usual way.

nlin.CD↗