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How to Optimally Charge a Battery: a Non Convex Singular Stochastic Control Problem (joint with Tiziano De Angelis and John Moriarty)

ABSTRACT: The known equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping (see, for example, Karatzas and Shreve (1984)) is not guaranteed if the performance criterion is not convex. The aim of this paper is to investigate how connections of this type generalise to a non convex storage-consumption problem for electricity, an unusual commodity with both positive and negative prices in some markets.

Our setting 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 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.

News

Defense

BiGSEM student Kerstin Hötte will defend her doctoral thesis. It will take place on Wednesday April 15, 2020 at 12:00 pm.

Defense

Torben Koch successfully defended his thesis on "On some Stochastic Control Problems arising in Environmental Economics and Commodity Markets".

Congratulations!

'Research Seminar Management' Talk

On January 28, there will be a 'Research Seminar Management' talk in U3-140 starting from 3:00 p.m. The speaker will be Prof. Shashi Matta (https://ekvv.uni-bielefeld.de/blog/wiwi/entry/vortrag_von_prof_shashi_matta)

Victor Zapata Garcia

Victor Garcia Zapata successfully defended his thesis on "Essays on Labour Economics and International Trade".

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Defense

BiGSEM student Victor Zapata Garcia will defend his doctoral thesis. It will take place in U3-140 at 1:00 pm on Monday January 13.