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.
