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A. K. Dixit and R. S. Pindyck, “Investment under Uncertainty,” Princeton University Press, Princeton, 1994.

has been cited by the following article:

  • TITLE: Energy Portfolio Management with Entry Decisions over an Infinite Horizon

    AUTHORS: Zhen Liu

    KEYWORDS: Energy Portfolio Management; Geometric Brownian Motion; Optimal Stopping

    JOURNAL NAME: Applied Mathematics, Vol.3 No.7, June 21, 2012

    ABSTRACT: We study a firm that has a conventional plant and considers introducing a new plant as an alternative to generate electricity. The firm’s decision includes the optimal entry time for the new plant, and the optimal dispatch between the existing plant and the new plant after it has been constructed to maximize the expected profit over an infinite time horizon. Under geometric Brownian motion, we formulate the problems as non-regular mixed optimal stopping/control problem. Due to the intractability of the mixed problem, we decompose it into two auxiliary problems, and characterize the optimal strategies in closed-form by standard value-matching and smooth-pasting conditions. Our numerical example confirms our theoretical results.