Application of conditional set theory to stochastic optimization

条件集理论在随机优化中的应用

• 批准号: 280192224
• 负责人: Professor Dr. Michael Kupper
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/280192224?language=en
• 关键词: Application; conditional; set; theory; stochastic

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.

我们将利用条件集理论研究随机优化问题。条件集理论允许处理局部结构，例如，出现在动态和稳健的金融市场模型。该方法是在[33]中发展的，作为[35]中开始的拓扑L0-模结果的推广。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等领域。在这个建议中，我们提出了一个工作计划的应用随机优化问题的动机是在金融市场的波动不确定性的平衡模型和控制问题。

项目成果

A transfer principle for second-order arithmetic, and applications

• DOI: 10.4115/jla.2018.10.8
• 发表时间: 2018-04
• 期刊: J. Log. Anal.
• 作者: M. Carl;Asgar Jamneshan

Exponential utility maximization under model uncertainty for unbounded endowments

• DOI: 10.1214/18-aap1428
• 发表时间: 2016-10
• 期刊: The Annals of Applied Probability
• 作者: Daniel Bartl

Measures and Integrals in Conditional Set Theory

• DOI: 10.1007/s11228-018-0478-3
• 发表时间: 2017-01
• 期刊: Set-Valued and Variational Analysis
• 影响因子: 1.6
• 作者: Asgar Jamneshan;Michael Kupper;Martin Streckfuß

Multidimensional quadratic BSDEs with separated generators

具有分离生成器的多维二次 BSDE

• DOI: 10.1214/17-ecp87
• 发表时间: 2014-12
• 期刊: Electronic Communications in Probability
• 影响因子: 0.5
• 作者: Jamneshan Asgar;Kupper Michael;Luo Peng
• 通讯作者: Luo Peng