Novel Parametric and Non-Parametric Cross-Entropy Models and their Applications in Portfolio Analysis - Sharma, Retneer; Singh, Vikramjeet (Communications in Mathematics and Applications, 2025)
For real-world applications in the mathematical sciences, it is important to create adaptable models in probability spaces. Models that are too rigid or too limited typically don't show how unpredictable and complicated these systems really are. To solve this problem, we need families of random models that can make the analytical framework more flexible and strong. This work presents a collection of novel parametric and non-parametric discrete cross-entropy models aimed at improving flexibility while maintaining mathematical precision. The fundamental purpose of these models is to create a framework for creative optimization techniques that may be used across varied situations. The suggested cross-entropy models build on standard probability-based methods by adding new distance metrics that make it easier to judge uncertainty and unpredictability. These models are important in theory and also have evident real-world uses. We specifically concentrate on their use in portfolio analysis, emphasizing risk assessment and the best allocation of assets. By using the created models, we illustrate how investors and decision-makers may more correctly reflect fluctuations in risk and return, leading to better-informed strategies for investing under uncertainty. The research shows that you may use either parametric or non-parametric versions of the models, depending on what data you have and what assumptions you make about the situation. When distributional assumptions are true, parametric forms provide you structured and efficient estimates. When these assumptions are weak or don't exist, non-parametric forms give you more freedom. Together, they provide a complete toolset for addressing uncertainty in complex systems. This paper advances the development of cross-entropy-based models inside probability spaces and demonstrates their efficacy in financial decision-making, especially regarding portfolio risk assessment and optimization
Keywords: Divergence Measures, Cross Entropy Models, Portfolio optimization, Risk Measurement, Financial Decision Making