英文标题：
《A Non Convex Singular Stochastic Control Problem and its Related Optimal
Stopping Boundaries》
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作者：
Tiziano De Angelis, Giorgio Ferrari, John Moriarty
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最新提交年份：
2014
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英文摘要：
Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this paper is to investigate how far connections of this type generalise to a non convex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a non convex infinite time horizon SSC problem whose state consists of an uncontrolled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory. We analyse the geometry of the action and inaction regions by characterising their (optimal) boundaries. Unlike the case of convex SSC problems we find that the optimal boundaries may be both reflecting and repelling and it is natural to interpret the problem as one of SSC with discretionary stopping.
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中文摘要：
已知具有凸性能标准的奇异随机控制（SSC）问题与最佳停止相关问题之间的等价性，例如参见Karatzas和Shreve[SIAM J.control Optim.22（1984）]。本文的目的是研究这种类型的连接在多大程度上推广到购电的非凸问题。在经典等价性失效的地方，我们提供了最优停止问题的替代连接。我们考虑了一个非凸无限时域SSC问题，其状态由一个代表实值商品价格的非受控扩散和一个代表库存的受控增长有界过程组成。我们通过描述其（最佳）边界来分析行动和不行动区域的几何结构。与凸SSC问题的情况不同，我们发现最优边界可能是反射和排斥的，将该问题解释为具有任意停止的SSC问题是自然的。
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分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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