Advanced Operator Theory for Energy Market Trading: A New Framework

This paper analyzes a parabolic operator (Formula presented.) that generalizes several well-known operators commonly used in financial mathematics. We establish the existence and uniqueness of the Feller semigroup associated with (Formula presented.) 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.