Application of conditional set theory to stochastic optimization

我们将利用条件集理论来研究随机优化问题。条件集合论允许处理局部结构，例如，在动态和稳健的金融市场模型中出现的局部结构。该方法是在[33]中发展起来的，是在[35]中提出的拓扑学L0-模的结果的推广。条件集理论已经成功地应用于条件风险度量理论、决策理论、均衡定价和倒向随机微分方程。在这项建议中，我们提出了一个应用于随机优化问题的工作方案，这些问题是由均衡模型和波动不确定性金融市场中的控制问题所驱动的。

We will study stochastic optimization problems by means of the conditional set theory. Conditional set theory allows to deal with local structures which, for instance, arise in dynamic and robust financial market models. The method is developed in [33] as an extension of the results in topological L0-modules, initiated in [35]. Conditional set theory has already been successfully applied to conditional risk measure theory, decision theory, equilibrium pricing and backward stochastic differential equations. In this proposal we suggest a work programme for applications to stochastic optimization problems which are motivated by equilibrium models and control problems in financial markets with volatility uncertainty.