This project investigates the role of fund flows and fees in portfolio choice and asset pricing. The main focus is on (i) understanding how these aspects fit in the existing theory, (ii) developing theoretical tools that make them tractable, and (iii) evaluating the departures from classical results due to flows and fees. Central issues are the extension of duality theory, and the development of asymptotic techniques in the long-horizon and small-fees limits.

This research aims to incorporate fund flows and fees - two central aspects of financial intermediation - in mathematical models of financial markets, to understand their agency effects on asset allocation, and their implications for welfare and pricing. This project will help understand the role of financial intermediaries, the incentives created by their fee-based contracts, and their interaction with investors' response through flows, that is subscriptions and redemptions.

Project Report

This project investigated optimal investment problems in which trading is costly because prices differ for buying and selling, execution prices depend on trading speed, or management fees are present. These problems depart from the classical theory, in which investors’ actions are assumed not to affect prices. A major contribution of the project is to have offered novel tractable methods to solve optimal investment problems through explicit formulas and asymptotic methods, which have expanded the range of models and questions that can be tackled. A central theme is that the long-horizon regime is an important tool to make problems tractable by focusing on the stationary tradeoffs of a model, without sacrificing its dynamic nature, and obtaining results that are robust to changes in both the horizon and preferences. The project has investigated the effect on managers of incentives such as stock and option grants or performance fees. A consequence of the robustness of long-horizon portfolios is that incentives, which induce perturbations in preferences, tend to lose their strength as the horizon increases. Robust option incentives are possible, but require several exercise prices. The broader impacts of this project include training of PhD students (including a female researcher) who have been supported as research assistants, and after graduation have taken academic positions in Financial Mathematics, thereby contributing to the development of science careers, including for women.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Henry A. Warchall
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Boston University
United States
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