Convex duality for stochastic singular control problems
Convex duality for stochastic singular control problems
复制标题
随机奇异控制问题的凸对偶性
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
H. Kauppila
中科院分区：
文献类型：
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作者：
P. Bank;H. Kauppila
我们为某些奇异控制问题发展了一个一般的凸对偶理论，将Kramkov和Schachermayer（1999）关于非负随机变量的最优期望效用的抽象结果推广到增加的自适应控制的最优期望效用水平。主要贡献是制定一个合适的对偶框架，识别问题的对偶功能以及充分的对偶性的原始和对偶值函数及其优化。我们的结果的范围说明了一个不可逆的投资问题和Hindy-Huang-Kreps效用最大化问题的不完全金融市场。
We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer (1999) for optimal expected utility from nonnegative random variables to the level of optimal expected utility from increasing, adapted controls. The main contributions are the formulation of a suitable duality framework, the identification of the problem's dual functional as well as the full duality for the primal and dual value functions and their optimizers. The scope of our results is illustrated by an irreversible investment problem and the Hindy-Huang-Kreps utility maximization problem for incomplete financial markets.