PPP项目多阶段投资时机决策的最优多停时模型及数值求解

THE OPTIMAL MULTIPLE STOPPING TIME MODEL AND NUMERICAL SOLUTION TO MUILTI-STAGE INVESTMENT TIMING DECISION OF PPP PROJECTS

研究需求不确定下PPP（Public Private Partnership,政府与社会资本合作）项目的多阶段投资时机决策问题,该问题有一定的实践意义和理论价值.利用最优多停时理论,建立了社会资本方的最优扩建时机决策模型.与一般美式期权的最优停时模型相比,该模型的求解难点有两方面：一是各阶段投资收益是路径依赖的,需求解一系列微分方程;二是扩建时机决策是最优多停时问题,需求解多个执行边界.用有限差分法对各阶段投资收益满足的微分方程进行数值求解,用多最小二乘蒙特卡洛方法对多阶段扩建时机决策求解.通过数值算例,对项目价值进行定价并给出了社会资本方的多阶段扩建最优执行边界,讨论了参数关于最优执行边界的灵敏性.

This paper investigates the investment timing decision of multi-stage PPP（Public Private Partnership） projects under uncertain demand. The optimal expansion timing decision of multi-stage investments is modeled by the ＂optimal multiple stopping time＂ theory. Comparing with the stopping time model for general American option, there are two difficulties in the computation. First, the investment revenues at all stages are path dependent, and a series of differential equations should be solved for these investment revenues. Second, the decision of expansion timing is an optimal multiple stopping time problem, and multiple execution boundaries need to be provided. The differential equations of investment revenues are solved by finite difference method, and the optimal expansion timing is obtained using Multi-least Squares Monte Carlo simulation. The project value is priced in a numerical example, and the concessionaire＇s optimal expansion strategies are also presented. Finally, the influences of model parameters on the expansion strategies are analyzed.