A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs

De Angelis T, Ferrari G, Moriarty J (2019)
MATHEMATICS OF OPERATIONS RESEARCH 44(2): 512-531.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
De Angelis, Tiziano; Ferrari, GiorgioUniBi; Moriarty, John
Abstract / Bemerkung
In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control, and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there.
Stichworte
finite-fuel singular stochastic control; optimal stopping; free; boundary; Hamilton-Jacobi-Bellman equation; irreversible investment; electricity market
Erscheinungsjahr
2019
Zeitschriftentitel
MATHEMATICS OF OPERATIONS RESEARCH
Band
44
Ausgabe
2
Seite(n)
512-531
ISSN
0364-765X
eISSN
1526-5471
Page URI
https://pub.uni-bielefeld.de/record/2936024

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De Angelis T, Ferrari G, Moriarty J. A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs. MATHEMATICS OF OPERATIONS RESEARCH. 2019;44(2):512-531.
De Angelis, T., Ferrari, G., & Moriarty, J. (2019). A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs. MATHEMATICS OF OPERATIONS RESEARCH, 44(2), 512-531. doi:10.1287/moor.2018.0934
De Angelis, T., Ferrari, G., and Moriarty, J. (2019). A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs. MATHEMATICS OF OPERATIONS RESEARCH 44, 512-531.
De Angelis, T., Ferrari, G., & Moriarty, J., 2019. A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs. MATHEMATICS OF OPERATIONS RESEARCH, 44(2), p 512-531.
T. De Angelis, G. Ferrari, and J. Moriarty, “A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs”, MATHEMATICS OF OPERATIONS RESEARCH, vol. 44, 2019, pp. 512-531.
De Angelis, T., Ferrari, G., Moriarty, J.: A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs. MATHEMATICS OF OPERATIONS RESEARCH. 44, 512-531 (2019).
De Angelis, Tiziano, Ferrari, Giorgio, and Moriarty, John. “A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs”. MATHEMATICS OF OPERATIONS RESEARCH 44.2 (2019): 512-531.