Abstract
We study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final wealth. The manager observes the prices but not the values of the market price of risk that drives the expected returns. The estimates of the market price of risk get more precise as more observations are available. We formulate the problem as an optimization under partial information. The particular structure of the incentives makes the objective function not concave. We solve the problem via the martingale method and, with a concavification procedure, we obtain the optimal wealth and the investment strategy. A numerical example shows the effect of learning on the optimal strategy.
Highlights
The reward of a fund manager usually increases when the Asset Under Management (AUM) grows, while it decreases when the AUM shrinks
The partial information case in a delegated portfolio management has been considered in the recent literature by Barucci and Marazzina (2015) in a slightly different setting compared to ours, where market is subject to two regimes, modelled via a continuous time two-state Markov chain and in Huang et al (2012) where investment learning is studied under a Bayesian approach
We studied a portfolio optimization problem for a manager who is compensated according to the performance of her portfolio relative to a benchmark
Summary
The reward of a fund manager usually increases when the Asset Under Management (AUM) grows, while it decreases when the AUM shrinks. An important feature of our setting is that, while the market of claims contingent to the knowledge of the market price of risk is incomplete, the market restricted to those claims contingent only to stock prices is instead complete We will exploit this fact to solve the optimization problem applying a martingale approach with the unique equivalent martingale measure (under the restricted setting) and using a concavification argument to determine the unique optimal solution. Both problems of relative incentives and of optimization under partial information have been separately addressed in many papers
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