Application of Integrable Systems in Carbon Price Determination

This paper examines carbon emission allowances and pricing mechanisms in the context of climate change, utilizing nonlinear evolution equation theory. Through empirical analysis of European Union EUA option data using the EGARCH model, the study identifies non-normal distribution characteristics in carbon market returns and explores how policy innovations influence price fluctuations. A key contribution is its application of soliton theory to analyze carbon price dynamics. By employing integrable systems like the (1 + 1)-dimensional Boussinesq equation, it aims to develop a mathematical model for carbon price stability. The research calculates the Lax pair for this system and uses Hirota’s bilinear method among other techniques to investigate whether carbon prices can exhibit soliton phenomena with consistent waveforms and amplitudes. This work provides insights into the carbon market’s dynamics and lays a theoretical foundation for better simulation, market behavior prediction, and optimization of climate policies.