A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES
De Angelis, Tiziano
Ferrari, Giorgio
Moriarty, John
finite-fuel singular stochastic control
optimal stopping
boundary
free
smooth fit
Hamilton-Jacobi-Bellmann equation
irreversible
investment
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.
Society For Industrial And Applied Mathematics
2015
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/2766940
De Angelis T, Ferrari G, Moriarty J. A NONCONVEX SINGULAR STOCHASTIC CONTROL PROBLEM AND ITS RELATED OPTIMAL STOPPING BOUNDARIES. <em>SIAM Journal on Control and Optimization</em>. 2015;53(3):1199-1223.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1137/14096801X
info:eu-repo/semantics/altIdentifier/issn/0363-0129
info:eu-repo/semantics/altIdentifier/wos/000357413400004
info:eu-repo/semantics/closedAccess