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...

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions,...

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian...

In this paper we establish a new connection between a class of 2-player nonzerosum games of optimal stopping and certain 2-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at two separate boundaries, then...

A problem of optimally purchasing electricity at a real-valued spot price (that is, with potentially negative cost) has been recently addressed in De Angelis, Ferrari and Moriarty (2015) [SIAM J. Control Optim. 53(3)]. This problem can be considered one of irreversible investment with a cost...

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian...

Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that...