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Journal of Undergraduate Research

Keywords

investor-manager conflict, dynamic models, marketshare incentives

College

Physical and Mathematical Sciences

Department

Mathematics

Abstract

In this project, my goal was to analyze the relation between marketshare incentives and risk taking in the hedge fund industry. Using the techniques of stochastic optimal control or dynamic programming, as applied in the typical Continuous-Time Consumption and Portfolio Choice model, I worked to develop a mathematical model to explore the effects of management fees and performance bonuses as well as the effects of changing market share on the fund manager’s implicit aversion towards high-risk portfolios. My continuing hypothesis is that due to fundamental differences between the investors and managers incentives, (essentially profit maximization vs. commission maximization) a fund manager will at times make sub-optimal or overly-risky investments which are not in the best interest of the investor. Over the course of my research I was able to make progress in solving the model and derived the conditions which describe the solution, but the partial differential equation that described the solution was too unruly and I am still working on a numerical solution (or at least analyzing the solution’s properties). However, I am planning on some simplifications to the model but, also, I have discovered a better method through which to model the problem. In this final report I will explain more about the problem, describe my accomplishments, and retell some of the invaluable experiences that I’ve had through the opportunity that ORCA and its donors have provided me.

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Mathematics Commons

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