Mathematical Models for Delegated Portfolio Management

该项目涉及两个主题：㈠研究管理其项目或投资组合风险的管理人员的最佳报酬，并研究有这些管理人员在场的金融市场价格形成情况;（ii）对于提供共同基金的公司，研究向投资者提供何种基金是最佳的，以何种费用和合同特征来满足不同信仰的投资者的需求，风险偏好和消费需求。关于主题（i）的研究结果将有助于了解哪种类型的薪酬计划最适合管理公司或投资组合风险的管理人员，并了解管理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投资费用。调查结果将揭示在监管高管薪酬、监管对冲基金和共同基金或向基金客户提供建议时应关注哪些问题。鉴于2007/2008年金融危机的原因之一是管理人员的薪酬方式，这一研究路线是有意义的。此外，由于这场危机，金融市场面临新的变化和挑战，必须保持和改善对这一领域青年研究人员的培训和支持，因为他们将在今后应对这些挑战方面发挥重要作用。这将有助于支持和培训学生从事这一项目。在更技术性的术语，这一项目将：（a）使用随机分析的最新进展，以发展一个最佳合同的一般理论，包括承包经理人管理其项目的风险的情况下，并将其应用于存在委托投资组合管理的均衡资产定价问题;（B）颠倒管理者和投资者的角色，从管理者的角度解决合同问题：如何最佳地构建向具有异质特征的投资者提供的基金菜单。从经济学的角度来看，主题（a）将部分弥补合同理论中的一个空白：大多数动态模型只考虑管理者对项目回报的影响，而不考虑其风险。在方法论上，它需要推广二阶倒向随机微分方程最近成熟的数学结果。 主题（B）将涵盖另一个空白：大多数合同文献假设投资者向经理人提供“要么接受，要么放弃”的合同。然而，在金融实践中，通常是另一种方式-对冲基金或共同基金家族提供他们的服务与精确的合同特征。从方法论上讲，它需要解决困难的动态逆向选择问题，有时制定为变分问题，有时减少到研究倒向随机微分方程和相关的偏微分方程。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.