Exact Solutions Of Stochastic KdV Equations And Its Application In Carbon Emission Pricing

Carbon neutrality is an essential issue of common concern for countries worldwide.Carbon pricing is an essential means to promote the achievement of carbon neutrality goals.The carbon pricing mechanism plays a crucial role in the operation of the carbon emission trading market.Studying the price fluctuations in the market and scientifically and reasonably pricing carbon assets is the key to the healthy and orderly development of the market.A relatively complete theoretical system has been formed regarding asset pricing.The application of soliton theory to carbon asset pricing is a new attempt.After a long period of propagation,collision,and separation,soliton waves will still return to their initial shape and velocity,which is very similar to the mean reversion phenomenon of financial market price fluctuations and can be used as a basis for studying carbon emissions pricing.In this thesis,we study the exact solutions of the stochastic KdV equation and their application in carbon emissions pricing.Firstly,the problem of exact solutions for the stochastic KdV equation is studied.Using the Darboux transformation method,various analytical solutions with stochastic terms are explicitly constructed,such as soliton solutions,positive and negative solutions,their interaction solutions,and rational solutions.It is found that under Gaussian white noise interference,the shape of the soliton solution remains unchanged.Then,based on empirical analysis of EU carbon emission quota price data,the existence of mean reversion in the carbon price series is confirmed,and the period and amplitude of mean reversion are explored.Using soliton waves for carbon emissions pricing,it is concluded that the single soliton solution of the stochastic KdV equation can be used to seek the central value of carbon emission rights,and its theoretical price is 71.48 euros/ton,which is consistent with the actual price of carbon emission rights.