Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem

Koch T, Vargiolu T (2019) Center for Mathematical Economics Working Papers; 627.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht| Englisch
 
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Autor/in
Koch, TorbenUniBi; Vargiolu, Tiziano
Abstract / Bemerkung
We consider a price-maker company which generates electricity and sells it in the spot market. The company can increase its level of installed power by irreversible installations of solar panels. In absence of the company's economic activities, the spot electricity price evolves as an Ornstein-Uhlenbeck process, and therefore it has a mean-reverting behavior. The current level of the company's installed power has a permanent impact on the electricity price and affects its mean-reversion level. The company aims at maximizing the total expected profits from selling electricity in the market, net of the total expected proportional costs of installation. This problem is modeled as a *two-dimensional degenerate singular stochastic control problem* in which the installation strategy is identified as the company's control variable. We follow a *guess-and-verify approach* to solve the problem. We find that the optimal installation strategy is triggered by a curve which separates the *waiting region*, where it is not optimal to install additional panels, and the *installation region*, where it is. Such a curve depends on the current level of the company's installed power, and is the unique strictly increasing function which solves a first-order ordinary differential equation (ODE). Finally, our study is complemented by a numerical analysis of the dependency of the optimal installation strategy on the model's parameters.

MSC2010 subject classification: 93E20; 49L20; 91B70; 60G99
Stichworte
singular stochastic control; irreversible investment; variational inequality; Ornstein-Uhlenbeck process; market impact
Erscheinungsjahr
2019
Band
627
Seite(n)
29
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2938811

Zitieren

Koch T, Vargiolu T. Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem. Center for Mathematical Economics Working Papers. Vol 627. Bielefeld: Center for Mathematical Economics; 2019.
Koch, T., & Vargiolu, T. (2019). Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem (Center for Mathematical Economics Working Papers, 627). Bielefeld: Center for Mathematical Economics.
Koch, T., and Vargiolu, T. (2019). Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem. Center for Mathematical Economics Working Papers, 627, Bielefeld: Center for Mathematical Economics.
Koch, T., & Vargiolu, T., 2019. Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem, Center for Mathematical Economics Working Papers, no.627, Bielefeld: Center for Mathematical Economics.
T. Koch and T. Vargiolu, Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem, Center for Mathematical Economics Working Papers, vol. 627, Bielefeld: Center for Mathematical Economics, 2019.
Koch, T., Vargiolu, T.: Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem. Center for Mathematical Economics Working Papers, 627. Center for Mathematical Economics, Bielefeld (2019).
Koch, Torben, and Vargiolu, Tiziano. Optimal Installation of Solar Panels with Price Impact: a Solvable Singular Stochastic Control Problem. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 627.
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2019-11-13T09:19:33Z
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