Stochastic and Robust Optimization Approaches for Financial and Operations Engineering

财务和运营工程的随机鲁棒优化方法

• 批准号: RGPIN-2014-04535
• 负责人: Kwon, Roy
• 金额: $ 1.6万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=656208
• 关键词: Stochastic; Robust; Optimization; Approaches; Financial

The classical optimization frameworks that serve as the basis for modeling in finance and operations management domains are often insightful and tractable. However, they often lack many significant real world aspects such as uncertainty. For example, the most common financial portfolio model used in industry is the mean-variance optimization (Markowitz) model, which is a deterministic problem and assumes that the expected prices(returns) of financial assets are known, which is not a practical assumption. In addition, other facets of real world environments when incorporated renders such models computationally intractable such as transaction costs or operational design decisions . Perhaps most importantly, decisions have to be made before parameter values are fully known and so the proper framework is to consider models that incorporate uncertainty to enable decisions that are immune or robust to uncertainty inherent in important parameters in the models. However, the consideration of both uncertainty and real world constraints results in models that are very challenging to solve. This proposal seeks to develop models and find solution methods for important financial engineering problems and operations management problems that integrate both uncertainty and real world practical constraints. In particular, the proposed research program seeks to investigate stochastic programming and robust optimization approaches for financial index tracking and spare parts management. The real world is inherently noisy and optimal robust solutions have a structure that is different than models that considers parameters to be deterministic and the proposal seeks to investigate what the appropriate optimal or approximate policies are in random environments. Algorithmic development is also an important component of the proposed research and will involve ideas from structured decomposition and robust convex optimization.

作为财务和运营管理领域建模基础的经典优化框架通常富有洞察力且易于处理。然而，它们通常缺乏许多重要的现实世界方面，例如不确定性。例如，业界最常见的金融投资组合模型是均值方差优化（Markowitz）模型，这是一个确定性问题，假设金融资产的预期价格（回报）已知，这不是一个实际的假设。此外，现实世界环境的其他方面在合并时使得此类模型在计算上难以处理，例如交易成本或操作设计决策。也许最重要的是，必须在完全了解参数值之前做出决策，因此正确的框架是考虑包含不确定性的模型，以实现对模型中重要参数固有的不确定性免疫或稳健的决策。然而，同时考虑不确定性和现实世界的约束会导致模型求解起来非常具有挑战性。该提案旨在为重要的金融工程问题和运营管理问题开发模型并寻找解决方法，将不确定性和现实世界的实际约束结合起来。特别是，拟议的研究计划旨在研究财务指数跟踪和备件管理的随机规划和稳健优化方法。现实世界本质上是嘈杂的，最优鲁棒解决方案的结构不同于将参数视为确定性的模型，该提案旨在研究随机环境中适当的最优或近似策略是什么。算法开发也是拟议研究的重要组成部分，并将涉及结构化分解和鲁棒凸优化的思想。