Journal of Applied Probability

Investing and stopping

Moritz Duembgen and L. C. G. Rogers

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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.

Article information

J. Appl. Probab., Volume 51, Number 4 (2014), 898-909.

First available in Project Euclid: 20 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60]

Optimal investment optimal stopping Brownian motion


Duembgen, Moritz; Rogers, L. C. G. Investing and stopping. J. Appl. Probab. 51 (2014), no. 4, 898--909.

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