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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 被引量:1

THE OPTIMAL MULTIPLE STOPPING TIME MODEL AND NUMERICAL SOLUTION TO MUILTI-STAGE INVESTMENT TIMING DECISION OF PPP PROJECTS
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摘要 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.
作者 张书华 李景焕 李瑜 Zhang Shuhua;Li Jinghuan;Li Yu(Coordinated Innovation Center for Computable Modeling in Management Science,Tianjin University of Finance and Economics,Tianjin 300222,Chin;Coordinated Innovation Center for Computable Modeling in Management Science,Tianjin University of Finance and Economics,Tianjin 300222,China;College of Science,Tianjin University of Commerce,Tianjin 300134,China;Coordinated Innovation Center for Computable Modeling in Management Science,Tianjin University of Finance and Economics,Tianjin 300222,China)
出处 《数值计算与计算机应用》 2018年第3期205-216,共12页 Journal on Numerical Methods and Computer Applications
基金 国家自然科学基金重大研究计划项目(91430108) 国家自然科学基金项目(11771322,71471132,71573189) 天津市教委科研计划项目成果(2017SK076,柔性合约视角下PPP项目投资与收益风险分担动态决策机制研究 2017KJ236,随机库存控制问题中HJB方程的多层校正方法) 天津市自然科学基金项目(17JCTPJC54800)
关键词 PPP项目 多阶段投资 最优多停时 有限差分 蒙特卡洛模拟 PPP projects multi-stage investment optimal multiple stopping time fi-nite difference Monte Carlo simulation
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