A solvable two-dimensional singular stochastic control problem with non convex costs - Tiziano De Angelis; Giorgio Ferrari; John Moriarty (Bielefeld University, Center for Mathematical Economics (IMW), 2016)
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 motion. We find analytical expressions for the value function, the optimal control and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there.
urn:nbn:de:0070-pub-29047299
Keywords: 330; finite-fuel singular stochastic control; optimal stopping; free boundary; Hamilton-Jacobi-Bellman equation; irreversible investment; electricity market