Mathematical Methods for Flexible Planning of Infrastructure Investment Projects under Uncertainty

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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.