### A Knightian Irreversible Investment Problem

Ferrari G, Li H, Riedel F (2020) Center for Mathematical Economics Working Papers; 634.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch

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Abstract / Bemerkung
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.

MSC2010 subject classification: 93E20, 91B38, 65C30
Stichworte
irreversible investment; Knightian uncertainty; singular stochastic control; base capacity policy; first-order conditions for optimality; backward equations
Erscheinungsjahr
2020
Serientitel
Center for Mathematical Economics Working Papers
Band
634
Seite(n)
33
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2942252

### Zitieren

Ferrari G, Li H, Riedel F. A Knightian Irreversible Investment Problem. Center for Mathematical Economics Working Papers. Vol 634. Bielefeld: Center for Mathematical Economics; 2020.
Ferrari, G., Li, H., & Riedel, F. (2020). A Knightian Irreversible Investment Problem (Center for Mathematical Economics Working Papers, 634). Bielefeld: Center for Mathematical Economics.
Ferrari, G., Li, H., and Riedel, F. (2020). A Knightian Irreversible Investment Problem. Center for Mathematical Economics Working Papers, 634, Bielefeld: Center for Mathematical Economics.
Ferrari, G., Li, H., & Riedel, F., 2020. A Knightian Irreversible Investment Problem, Center for Mathematical Economics Working Papers, no.634, Bielefeld: Center for Mathematical Economics.
G. Ferrari, H. Li, and F. Riedel, A Knightian Irreversible Investment Problem, Center for Mathematical Economics Working Papers, vol. 634, Bielefeld: Center for Mathematical Economics, 2020.
Ferrari, G., Li, H., Riedel, F.: A Knightian Irreversible Investment Problem. Center for Mathematical Economics Working Papers, 634. Center for Mathematical Economics, Bielefeld (2020).
Ferrari, Giorgio, Li, Hanwu, and Riedel, Frank. A Knightian Irreversible Investment Problem. Bielefeld: Center for Mathematical Economics, 2020. Center for Mathematical Economics Working Papers. 634.
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