权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Mathematical Models for Delegated Portfolio Management

委托投资组合管理的数学模型

基本信息

批准号：
1810807
负责人：
Jaksa Cvitanic
金额：
$ 26.08万
依托单位：
California Institute of Technology
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1810807&HistoricalAwards=false
关键词：
Mathematical Models Delegated Portfolio Management

项目摘要

This project addresses two topics: (i) studying optimal compensation of managers who manage the risk of their projects or portfolios, and studying price formation in financial markets in the presence of such managers; (ii) for a firm offering mutual funds, studying what kind of funds are optimal to offer to investors, with what fees and contracting features, to satisfy the demand of investors of varying beliefs, risk preferences and consumption needs. The findings on topic (i) will help understand which type of compensation schemes are optimally offered to managers that manage risk of companies or portfolios, and to understand the effect of managerial compensation on the formation of asset prices. The findings on topic (ii) will explain how fund families structure their offerings and the associated investment fees. The findings will shed light on which issues to focus on when regulating compensation of executives, or regulating hedge funds and mutual funds, or giving advice to fund customers. This line of research is of interest given that one of the reasons for the 2007/2008 financial crisis was the way managers had been compensated. Moreover, because of the crisis, new changes and challenges are facing financial markets and it is important to maintain and improve the training and support available to young researchers in this field, as they will play an important role in facing those challenges in the future. This will be helped by supporting and training students working on this project.In more technical terms, this project will: (a) use recent advances in Stochastic Analysis to develop a general theory of optimal contracting that includes the case of contracting managers who manage the risk of their projects, and apply it to the problem of equilibrium asset pricing in the presence of delegated portfolio management; (b) reverse the roles of managers and investors, and solve contracting problems from the perspective of managers: how to optimally structure the menu of funds offered to investors with heterogeneous features. From the economic point of view, topic (a) will partially cover a gap in contract theory: most of the dynamic models only the effect of the managers on project return, and not on its risk. Methodologically, it requires extending recent sophisticated mathematical results for second order Backward Stochastic Differential Equations. Topic (b) will cover another gap: most of the contract literature assumes that investors offer take-it-or-leave-it contracts to managers. However, in financial practice, it is usually other way round - hedge funds or mutual fund families offer their services with precise contracting features. Methodologically, it requires solving difficult dynamic adverse selection problems, sometimes formulated as calculus of variations problems, sometimes reduced to studying Backward Stochastic Differential Equations and associated Partial Differential Equations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个项目涉及两个主题：(I)研究管理其项目或投资组合风险的经理的最优薪酬，并在这些经理在场的情况下研究金融市场的价格形成；(Ii)对于提供共同基金的公司，研究向投资者提供哪种基金是最佳的，具有什么费用和合同特征，以满足不同信仰、风险偏好和消费需求的投资者的需求。主题(I)的研究结果将有助于理解向管理公司或投资组合风险的经理提供哪种类型的薪酬方案是最优的，并有助于理解管理层薪酬对资产价格形成的影响。关于主题(Ii)的调查结果将解释基金家族如何构建其产品和相关的投资费用。这些发现将阐明，在监管高管薪酬、监管对冲基金和共同基金、或向基金客户提供建议时，应该关注哪些问题。考虑到2007/2008年金融危机的原因之一是经理人获得薪酬的方式，这一研究路线很有意义。此外，由于危机，金融市场面临着新的变化和挑战，重要的是保持和改进这一领域对年轻研究人员的培训和支持，因为他们将在未来应对这些挑战方面发挥重要作用。这将有助于支持和培训从事这个项目的学生。在更专业的术语中，这个项目将：(A)利用随机分析的最新进展来发展最优收缩的一般理论，其中包括管理项目风险的收缩经理的情况，并将其应用于在委托投资组合管理存在的情况下的均衡资产定价问题；(B)颠倒经理和投资者的角色，并从经理的角度解决收缩问题：如何以最佳结构向投资者提供具有不同特征的基金菜单。从经济学的角度来看，话题(A)将部分弥补契约理论中的一个空白：大多数动态模型只考虑管理者对项目回报的影响，而不是对其风险的影响。在方法论上，它需要推广最近关于二阶倒向随机微分方程的复杂的数学结果。话题(B)将填补另一个空白：大多数合同文献假设投资者向经理提供要么接受要么放弃的合同。然而，在金融实践中，情况通常是相反的--对冲基金或共同基金家族提供的服务具有精确的合同特征。在方法论上，它需要解决困难的动态逆向选择问题，有时被表述为变分问题，有时被归结为研究倒向随机微分方程和相关的偏微分方程。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。