A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES

De Angelis T, Ferrari G, Moriarty J (2015)
SIAM Journal on Control and Optimization 53(3): 1199-1223.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping; see, for example, Karatzas and Shreve [SIAM J. Control Optim., 22 (1984), pp. 856-877]. The aim of this paper is to investigate how far connections of this type generalize to a nonconvex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a nonconvex infinite time horizon SSC problem whose state consists of an uncontrolled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory. We analyze the geometry of the action and inaction regions by characterizing their (optimal) boundaries. Unlike the case of convex SSC problems we find that the optimal boundaries may be both reflecting and repelling and it is natural to interpret the problem as one of SSC with discretionary stopping.
Erscheinungsjahr
Zeitschriftentitel
SIAM Journal on Control and Optimization
Band
53
Zeitschriftennummer
3
Seite
1199-1223
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De Angelis T, Ferrari G, Moriarty J. A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES. SIAM Journal on Control and Optimization. 2015;53(3):1199-1223.
De Angelis, T., Ferrari, G., & Moriarty, J. (2015). A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES. SIAM Journal on Control and Optimization, 53(3), 1199-1223. doi:10.1137/14096801X
De Angelis, T., Ferrari, G., and Moriarty, J. (2015). A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES. SIAM Journal on Control and Optimization 53, 1199-1223.
De Angelis, T., Ferrari, G., & Moriarty, J., 2015. A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES. SIAM Journal on Control and Optimization, 53(3), p 1199-1223.
T. De Angelis, G. Ferrari, and J. Moriarty, “A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES”, SIAM Journal on Control and Optimization, vol. 53, 2015, pp. 1199-1223.
De Angelis, T., Ferrari, G., Moriarty, J.: A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES. SIAM Journal on Control and Optimization. 53, 1199-1223 (2015).
De Angelis, Tiziano, Ferrari, Giorgio, and Moriarty, John. “A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES”. SIAM Journal on Control and Optimization 53.3 (2015): 1199-1223.
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Alte Ausgabe
A non convex singular stochastic control problem and its related optimal stopping boundaries
de Angelis T, Ferrari G, Moriarty J (2014) Center for Mathematical Economics Working Papers; 508.
Bielefeld: Center for Mathematical Economics.