Process-based risk measures and risk-averse control of discrete-time systems
Process-based risk measures and risk-averse control of discrete-time systems
复制标题
离散时间系统基于过程的风险度量和风险规避控制
DOI：
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复制
发表时间：
2014
影响因子：
2.7
通讯作者：
A. Ruszczynski
中科院分区：
文献类型：
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作者：
Jingnan Fan;A. Ruszczynski
对于受控离散时间随机过程，我们引入了一类新的动态风险度量，我们称之为基于过程的。它们的主要特征是，它们测量的过程的风险是基本过程的历史的函数。我们引入了一个新的概念，条件随机时间一致性，我们推导出结构的基于过程的风险措施享受这一属性。我们表明，它们可以等价地表示为一个集合的静态法律不变的风险措施的功能空间的基础过程的状态。我们将这一结果控制马尔可夫过程，我们推导出动态规划方程。我们还推导出动态规划方程的多阶段随机规划与决策相关的分布。
For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state of the base process. We apply this result to controlled Markov processes and we derive dynamic programming equations. We also derive dynamic programming equations for multistage stochastic programming with decision-dependent distributions.