Conference Agenda

We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish sufficient conditions for determining the optimality of the one-barrier strategy when the uncontrolled process $X$ follows a spectrally negative L\'evy process with a L\'evy measure defined by a completely monotone density. Secondly, to verify the optimality of the $(2n+1)$-barrier strategy when $X$ is a Brownian motion with a drift. Additionally, we provide an algorithm to compute the barrier values in the latter case.

We characterise Markov perfect equilibria in continuous time stochastic timing games in terms of an abstract coupled system of variational inequalities for the corresponding value functions. We provide conditions concerning regularity and construction of equilibria in the case of diffusions. We further investigate a non-trivial one-dimensional case where under relatively mild monotonicity conditions on the data it is possible to give a characterisation of a natural class of Markov perfect equilibria, and compute them numerically. The classical problem of pre-emption and rent equalisation is revisited from this perspective and we show that pre-emptive and war-of-attrition-like behaviour translate into different degrees of regularity of the value function at the stopping boundary.

We consider a power-to-heat energy system providing superheated steam for industrial processes. It consists of a high-temperature heat pump for heat supply, a wind turbine for power generation, a thermal energy storage to store excess heat and a steam generator. If the system's energy demand cannot be covered by electricity from the wind turbine, additional electricity must be purchased from the power grid.

For this system we investigate the cost-optimal management aiming to minimize the cost for electricity from the grid by a suitable combination of the wind power and the system's thermal storage. This is a decision making problem under uncertainties about the future prices for electricity from the grid and the future generation of wind power. The resulting stochastic optimal control problem is treated as finite horizon Markov Decision Process (MDP) for a multi-dimensional controlled state process.

We first consider the classical backward recursion techniques for solving the associated dynamic programming equation for the value function and compute the optimal decision rule. Since that approach suffers from the the curse of dimensionality we also apply Q-learning techniques that are able to provide a good approximate solution to the MDP within a reasonable computational time.