Dynamic Optimization in Management

管理动态优化

• 批准号: RGPIN-2015-06402
• 负责人: Breton, Michèle
• 金额: $ 2.04万
• 依托单位: HEC Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=614129
• 关键词: Dynamic; Optimization; Management

The objective of this research program is to develop mathematical models and efficient algorithms to solve practical decision-making problems that are dynamic in nature and that involve uncertainty. Two specific areas of application will be considered: investment decisions in financial markets, and the management of environmental and natural resources. Although these application areas are very different, they share a common methodological approach, that is, stochastic dynamic optimization in a multidimensional framework. In both cases, the solution of realistic problems requires the development of efficient numerical methods. Thus, in addition to addressing these specific issues, a broader objective of this research program is to develop innovative methods for the numerical solution of large-scale stochastic dynamic problems, and to contribute to the advancement of knowledge in the field of decision-making under uncertainty. The evaluation of innovative financial products almost always requires the use of numerical procedures. Moreover, financial institutions are increasingly concerned with managing risk and satisfying regulatory requirements. In practice, algorithms for the valuation of financial products, the evaluation of risk, and the determination of investment or hedging strategies need to be used in real time and should provide accurate results in seconds. The objectives of this first line of research are to increase the efficiency (accuracy, speed) of evaluation algorithms, and to develop new general approaches that can be used for more realistic market models. A growing concern in environmental and resources management is related to the so-called "tragedy of the commons". Access to a common resource (air quality, biodiversity, high-seas fishing, non-renewable resources) leads to overexploitation, and possibly, to catastrophic consequences. One of the means employed to prevent this from happening is the establishment of agreements between stakeholders. In this context, foresight is defined as the ability of stakeholders to account for the evolution over time of key features (environmental damage costs, learning, technological progress, signatories, economic development), when this evolution depends on agents' joint strategies. Clearly, dynamics and foresight are important factors in the design, stability and implementability of environmental agreements. The objectives of this second line of research is to study how agreements are affected by dynamics and uncertainty, and by the foresight and strategic outlook of participants. The general methodology considered is that of dynamic optimization with multidimensional state spaces. Solution approaches will include functional interpolation schemes (value functions and/or optimal strategies), and dimension reduction techniques, including aggregation of states, and learning (forward) algorithms.

该研究计划的目标是开发数学模型和有效的算法来解决实际的决策问题，这些问题在本质上是动态的，并且涉及不确定性。将考虑两个具体的应用领域：金融市场的投资决策，以及环境和自然资源的管理。虽然这些应用领域是非常不同的，他们有一个共同的方法，即在多维框架中的随机动态优化。在这两种情况下，现实问题的解决方案需要发展有效的数值方法。因此，除了解决这些具体问题，本研究计划的一个更广泛的目标是开发大规模随机动态问题的数值解的创新方法，并有助于在不确定性决策领域的知识进步。 创新金融产品的评估几乎总是需要使用数值程序。此外，金融机构越来越关注管理风险和满足监管要求。在实践中，金融产品的估值、风险评估以及投资或对冲策略的确定需要在真实的时间内使用算法，并且应该在几秒钟内提供准确的结果。第一条研究路线的目标是提高评估算法的效率（准确性，速度），并开发可用于更现实的市场模型的新的通用方法。 在环境和资源管理方面，人们越来越关注所谓的“公地悲剧”。获得共同资源（空气质量、生物多样性、公海捕鱼、不可再生资源）会导致过度开发，并可能造成灾难性后果。防止这种情况发生的手段之一是在利益攸关方之间达成协议。在这方面，远见被定义为利益攸关方说明关键特征（环境损害成本、学习、技术进步、签署方、经济发展）随时间演变的能力，而这种演变取决于行为方的联合战略。显然，动态和远见是环境协定的设计、稳定性和可执行性的重要因素。第二条研究路线的目标是研究协议如何受到动态和不确定性以及参与者的远见和战略前景的影响。 考虑的一般方法是多维状态空间的动态优化。解决方法将包括函数插值方案（值函数和/或最优策略）和降维技术，包括状态聚合和学习（前向）算法。