2002 Fiscal Year Final Research Report Summary
Mathematical Methods for Flexible Planning of Infrastructure Investment Projects under Uncertainty
| Project/Area Number |
13450206
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
交通工学・国土計画
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| Research Institution | Tohoku University |
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Principal Investigator |
AKAMATSU Takashi Graduate School of Information Sciences, Associate Professor, 大学院・情報科学研究科, 助教授 (90262964)
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| Co-Investigator(Kenkyū-buntansha) |
MORISUGI Hisayoshi Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (80026161)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Investment under Uncertainty / Real Options / Evaluation of Infrastructures / Incomplete Markets / Arbitrage Pricing / Variational Inequalities / Graph Structure / Stochastic Control |
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| Research Abstract |
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.
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