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A Knightian Irreversible Investment Problem

Giorgio Ferrari, Hanwu Li and Frank Riedel ()
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Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Hanwu Li: Center for Mathematical Economics, Bielefeld University

No 634, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic backward equation under the worst- case scenario. In a time-homogeneous setting { where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called "\$\kappa$ --ignorance" - we are able to provide the explicit form of the optimal irreversible investment plan.

Keywords: irreversible investment; Knightian uncertainty; singular stochastic control; base capacity policy; first-order conditions for optimality; backward equations (search for similar items in EconPapers)
Pages: 33
Date: 2020-04-01
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https://pub.uni-bielefeld.de/download/2942252/2942253 First Version, 2020 (application/pdf)

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Working Paper: A Knightian Irreversible Investment Problem (2020) Downloads
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