Mathematical Methods for Flexible Planning of Infrastructure Investment Projects under Uncertainty

本文提出了经济不确定性下基础设施投资/管理动态决策的框架和数学方法。具体来说，基础设施项目被定义为具有随机现金流的一束复杂期权（资产），并被表述为随机脉冲控制问题，其中控制变量具有相互依赖关系，以图结构表示。然后，我们重点研究了两个问题：(1)控制具有复杂链结构的期权束的活动；(2)评估基础设施管理问题中固有的“不完全市场（基础）风险”。对于前一个问题，我们揭示了(1)中表述的一类控制问题统一化为标准形式的非线性互补/变分不等式问题（NCP/VIP）；此外，我们表明，利用基于图论的分解方案和NCP/VIP变换方法的思想，可以非常有效地解决这些问题。对于后一个问题，我们提出了不完全市场中期权定价的一种新方法，该方法在无套利约束和kl -信息准则下估计了唯一鞅测度。我们证明了该问题等价于一类符合效用最大化框架的投资组合对冲问题。并给出了评估各种实物期权的有效算法。

This study presents a framework and mathematical methods for dynamic decision-makings of infrastructure investment/management under economic uncertainly. Specifically, an infrastructure project is defined as a bundle of complex options (assets) with stochastic cash flow streams, and is formulated as a stochastic impulse control problem in which control variables have interdependency represented as a graph-structure. We then focuses on two problems(1) controlling the activities of the bundle of options with complex chain-structure(2) evaluating "incomplete market (basis) risks" intrinsic in infrastructure management problems. For the former problem, we reveal that a family of control problems formulated in (1) reduces to a standard form Non-linear Complementarity/Variational Inequality problem (NCP/VIP) in a unified way; furthermore, we show that the problems can be solved very efficiently, exploiting the idea of graph-theory based decomposition schemes and the NCP/VIP transformation approach. For the latter problem, we propose a new approach for pricing options in incomplete markets, in which a unique martingale measure is estimated under the no arbitrage constraints and a KL-information criterion. We show that the problem is equivalent to a certain type of portfolio hedging problem consistent with the utility maximization framework. Efficient algorithms for evaluating various real options are also presented.