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December 2014 Investing and stopping
Moritz Duembgen, L. C. G. Rogers
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J. Appl. Probab. 51(4): 898-909 (December 2014).

Abstract

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.

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Moritz Duembgen. L. C. G. Rogers. "Investing and stopping." J. Appl. Probab. 51 (4) 898 - 909, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 1308.60045
MathSciNet: MR3301277

Subjects:
Primary: 60G40
Secondary: 62L15

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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