Journal of Applied Probability

Investing and stopping

Moritz Duembgen and L. C. G. Rogers

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

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

Dates
First available in Project Euclid: 20 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1421763316

Mathematical Reviews number (MathSciNet)
MR3301277

Zentralblatt MATH identifier
1308.60045

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

Keywords
Optimal investment optimal stopping Brownian motion

Citation

Duembgen, Moritz; Rogers, L. C. G. Investing and stopping. J. Appl. Probab. 51 (2014), no. 4, 898--909. https://projecteuclid.org/euclid.jap/1421763316


Export citation

References

  • Azéma, J. and Yor, M. (1979). Une solution simple au problème de Skorokhod. In Séminaire de Probabilités XIII, Springer, Berlin, pp. 90–115.
  • Cox, A. M. G. and Obloj, J. (2011). Robust hedging of double touch barrier options. SIAM J. Financial Math. 2, 141–182.
  • Dybvig, P. H. and Koo, H.-K. (1996). Investment with taxes. Working paper.
  • Goetzmann, W. N., Ingersoll, J. E. and Ross, S. A. (2003). High-water marks and hedge fund management contracts. J. Finance 58, 1685–1718.
  • Guasoni, P. and Obloj, J. (2013). The incentives of hedge fund fees and high-water marks. Math. Finance. Available at: doi: 10.1111/mafi.12057.
  • Rogers, L. C. G. (1993). The joint law of the maximum and terminal value of a martingale. Prob. Theory Relat. Fields 95, 451–466.