A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Non Convex Costs

T. Angelis, Giorgio Ferrari, J. Moriarty
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引用次数: 11

Abstract

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 and the smooth fit condition holds there.
具有非凸代价的二维退化奇异随机控制问题
本文给出了一类二维退化非凸奇异随机控制问题的完整理论分析。优化是由电力市场中的存储-消耗模型驱动的,并以布朗运动建模的随机实值现货价格为特征。我们找到了值函数、最优控制以及行动和不行动区域边界的解析表达式。最优策略用两个单调和不连续的排斥自由边界来表示,尽管其中一个边界的一部分是恒定的,并且光滑拟合条件在那里成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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