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Investing and Stopping

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  • Moritz Duembgen
  • L. C. G. Rogers

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.

Suggested Citation

  • Moritz Duembgen & L. C. G. Rogers, 2014. "Investing and Stopping," Papers 1403.0202, arXiv.org.
    • Handle: RePEc:arx:papers:1403.0202
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    References listed on IDEAS

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    1. William N. Goetzmann & Jonathan E. Ingersoll & Stephen A. Ross, 2003. "High‐Water Marks and Hedge Fund Management Contracts," Journal of Finance, American Finance Association, vol. 58(4), pages 1685-1718, August.
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