We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced. Our problem is one of storage and consumption for electricity, a partially storable commodity with both positive and negative prices in some markets, and has similarities to the finite fuel monotone follower problem. In particular we consider a non convex 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 analyse the geometry of the action and inaction regions by characterising the related optimal stopping boundaries .
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) . The aim of this paper is to investigate how far connections of this type generalise to a non convex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a non convex 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 analyse the geometry of the action and inaction regions by characterising 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 .
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We show that the equivalence between certain
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with convex performance criteria
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known for convex performance criteria (see, for example
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see for example
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SIAM J. Control Optim. 22
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) continues to hold in
. The aim of this paper is to investigate how far connections of this type generalise to
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provided a related discretionary stopping time is introduced. Our problem is one of storage and consumption for electricity, a partially storable commodity with both positive and negative prices in some markets, and has similarities to the finite fuel monotone follower problem. In particular we
of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We
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the related optimal stopping boundaries
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