A solvable two-dimensional singular stochastic control problem with non convex costs

de Angelis T, Ferrari G, Moriarty J (2016) Center for Mathematical Economics Working Papers; 561.
Bielefeld: Center for Mathematical Economics.

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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.
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de Angelis T, Ferrari G, Moriarty J. A solvable two-dimensional singular stochastic control problem with non convex costs. Center for Mathematical Economics Working Papers. Vol 561. Bielefeld: Center for Mathematical Economics; 2016.
de Angelis, T., Ferrari, G., & Moriarty, J. (2016). A solvable two-dimensional singular stochastic control problem with non convex costs (Center for Mathematical Economics Working Papers, 561). Bielefeld: Center for Mathematical Economics.
de Angelis, T., Ferrari, G., and Moriarty, J. (2016). A solvable two-dimensional singular stochastic control problem with non convex costs. Center for Mathematical Economics Working Papers, 561, Bielefeld: Center for Mathematical Economics.
de Angelis, T., Ferrari, G., & Moriarty, J., 2016. A solvable two-dimensional singular stochastic control problem with non convex costs, Center for Mathematical Economics Working Papers, no.561, Bielefeld: Center for Mathematical Economics.
T. de Angelis, G. Ferrari, and J. Moriarty, A solvable two-dimensional singular stochastic control problem with non convex costs, Center for Mathematical Economics Working Papers, vol. 561, Bielefeld: Center for Mathematical Economics, 2016.
de Angelis, T., Ferrari, G., Moriarty, J.: A solvable two-dimensional singular stochastic control problem with non convex costs. Center for Mathematical Economics Working Papers, 561. Center for Mathematical Economics, Bielefeld (2016).
de Angelis, Tiziano, Ferrari, Giorgio, and Moriarty, John. A solvable two-dimensional singular stochastic control problem with non convex costs. Bielefeld: Center for Mathematical Economics, 2016. Center for Mathematical Economics Working Papers. 561.
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