Solutions And Asymptotic Properties Of Freight Rate Model

The world economic environment is uncertain,and the fluctuation of freight rate in the shipping market also has the corresponding uncertainty.In order to obtain more profits in the uncertain market environment,shipping enterprises must understand the market demand,grasp the change law of freight rate,and timely adjust the structure of shipping capacity.With a good freight rate model,operators can better predict the change of freight rate,so as to make more reasonable decisions.At the beginning of the 21st century,some scholars such as Tvedt applied a series of financial models to the study of freight rates.Later,when attempting to find the relationship between traditional equilibrium market models and maritime asset pricing models,Tvedt comprehensively considered the dynamic relationships between multiple factors and established freight rate models using econometric methods.The article starts from studying the solution of the freight rate model proposed by Tvedt,generalizes and studies some properties of the model,and the research content mainly includes two parts.In the first part,when solving the freight rate model,the general law of the equation in this form is summarized;When extended to the general form,the integral factor method is used to transform the equation into a definite differential equation.Under certain conditions,this form can solve the Nonlinear Stochastic Differential Equation;Continue the extension of the model.At this time,the above integration factor method is still used,and the obtained form can only be used to solve the Linear Stochastic Differential Equation.If Lamperti transformation and CameronMartin-Girsanov theorem are used,under certain conditions,the weak solution of the equation can be obtained.In the second part,the asymptotic properties of the freight rate model with nonlinear fluctuations are studied.The stochastic ultimate boundedness of the solution is proved by using Chebyshev inequality;By taking an appropriate function,using exponential martingale inequality and Borel-Cantelli lemma,it is found that the orbit estimation of the solution is only related to the drift coefficient of the model.Finally,the model is simulated numerically to verify the rationality of the model.