Investing and Stopping

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but a...

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Bibliographic Details
Published in:Journal of applied probability 2014-12, Vol.51 (4), p.898-909
Main Authors: Duembgen, Moritz, Rogers, L. C. G.
Format: Article
Language:English
Subjects:
60G40
62L15
Approximation
Asset management
Brownian motion
Equivalence
Fees
Financial investments
Hedge funds
Investment advisors
Investment policy
Investment strategies
Investors
Martingales
Mathematical models
Mathematical problems
Optimal investment
optimal stopping
Optimization
Random walk
Random walk theory
Rectangles
Studies
Terminals
Citations: Items that this one cites
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Summary:In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but also on the lowest and the highest value reached over that time. We establish equivalence to an optimal stopping problem for Brownian motion; by approximating this problem with the corresponding optimal stopping problem for a random walk we are led to a simple and efficient numerical scheme to find the solution, which we then illustrate with some examples.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1421763316