Advanced Operator Theory for Energy Market Trading: A New Framework

Michele Bufalo () and Viviana Fanelli
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Michele Bufalo: Department of Economics, Management and Business Law, University of Bari Aldo Moro, via C. Rosalba, 70124 Bari, Italy
Viviana Fanelli: Department of Economics, University of Foggia, via R. Caggese, 71121 Foggia, Italy

Risks, 2025, vol. 13, issue 7, 1-21

Abstract: This paper analyzes a parabolic operator L that generalizes several well-known operators commonly used in financial mathematics. We establish the existence and uniqueness of the Feller semigroup associated with L and derive its explicit analytical representation. The theoretical framework developed in this study provides a robust foundation for modeling stochastic processes relevant to financial markets. Furthermore, we apply these findings to energy market trading by developing specialized simulation algorithms and forecasting models. These methodologies were tested across all assets comprising the S&P 500 Energy Index, evaluating their predictive accuracy and effectiveness in capturing market dynamics. The empirical analysis demonstrated the practical advantages of employing generalized semigroups in modeling non-Gaussian market behaviors and extreme price fluctuations.

Keywords: Feller semigroups; Feynman–Kac formula; energy markets (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:13:y:2025:i:7:p:118-:d:1683692

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