基于复杂性竞争扰动的铁路货运期权定价模型

针对铁路货运市场特征，利用二叉树刻画运输价格形成过程，引入带有不同运输方式复杂博弈机制的竞争因子，建立铁路货运期权定价模型；首先通过分析铁路局与客户群体利润函数的一阶条件，得到考虑分担率的最优期权执行价格；其次基于双层规划方法构建合约期内不同运输方式的价格竞争过程，在下层规划中采用累积前景理论与多主体强化学习机制刻画客户企业群体的复杂决策；通过数值仿真，分析了引入竞争因子后的运输期权价格变化与客户企业理性特征对各项价格的影响机理；研究发现：1）复杂竞争因子对铁路货运价格，期权执行价格及期权价值产生了明显扰动；2）客户企业的理性特征与最优期权执行价格及期权价值之间具有显著的变化规律，数值分析结果较好地验证了理论分析.

Option pricing model of railway freight transportation based on complex competition disturbance

According to the characteristics of rail freight market, the binomial tree model is used to describe the formation of freight price, competition factor with complex game mechanism of different transportation modes is introduced to establish a new rail freight option pricing model; Firstly, by analyzing the first-order condition of profit function between railway administration and customer enterprises, the optimal option execution price considering share rate is obtained; Secondly, the price competition process of different transportation modes in the contract period is constructed based on the bi-level programming, in the lower level programming, the theory of cumulative prospect is combined with the multi-agent reinforcement learning mechanism to describe the complex decision making of the customer enterprises; Through the numerical simulation, the price change of transportation options after the introduction of competition factors and the influence mechanism of customer enterprises' rational characteristics on various prices are analyzed; The results show that: 1) Complex competition factors have a significant impact on railway freight price, option execution price and option value; 2) There are significant changes between the rational characteristics of customer enterprises and the optimal option price and option value. The numerical analysis results verify the theoretical analysis well.