In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex 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.

A solvable two-dimensional degenerate singular stochastic control problem with nonconvex costs

De Angelis T.;
2019-01-01

Abstract

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex 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.
2019
44
2
512
531
http://arxiv.org/abs/1411.2428
Electricity market; Finite-fuel singular stochastic control; Free boundary; Hamilton–Jacobi–Bellman equation; Irreversible investment; Optimal stopping
De Angelis T.; Ferrari G.; Moriarty J.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1761966
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