Optimal Stopping in Higher Dimensions: The Case of Investments in the Sustainable Energy Transition

Frank Heinz and Reinhard Madlener
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Frank Heinz: frank.heinz@rwth-aachen.de

No No. 5/2025, FCN Working Papers from E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN)

Abstract: Real options analysis includes research on optimal stopping problems that is focusing largely on one-dimensional problems, or on multidimensional problems with analytically tractable payoff functions. However, many research questions addressing investments relevant to sustainable energy transition require optimal stopping with multiple uncertainties, in high time resolution, with general stochastic dynamics, and a general payoff function. These questions are difficult to answer with current theory. Thus, this work presents a new method for solving optimal stopping problems in this general setting. We adapted the Hamilton–Jacobi–Bellman equation to such problems, and then developed a numerical solution procedure. This approach was tested on the following real-world case: retrofitting an offshore wind farm with an electrolyzer, both operating under market-based electricity pricing. Such assets are challenging to assess because of their simultaneous exposure to a volatile electricity price and a volatile electricity production. In particular, the fluctuating electricity price facilitate profits, while at the same time, it constitutes a potentially investment-deterring uncertainty. Despite the method’s numerical complexity and computational demands, it proves effective and thus, broadens the applicability of real options analysis to this class of problems, providing a new analytical tool for research on the sustainable energy transition.

Keywords: Dynamic programming; Real options; Optimal stopping; Decision making under uncertainty (search for similar items in EconPapers)
JEL-codes: C61 D81 G11 (search for similar items in EconPapers)
Pages: 28
Date: 2025-03-01
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