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Investing and Stopping

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  30 January 2018

Moritz Duembgen  and
L. C. G. Rogers
Moritz Duembgen*
Affiliation:
University of Cambridge
L. C. G. Rogers*
Affiliation:
University of Cambridge
*
∗ Postal address: Statistical Laboratory, University of Cambridge, Cambridge CB3 0WB, UK. Email address: l.c.g.rogers@statslab.cam.ac.uk
∗ Postal address: Statistical Laboratory, University of Cambridge, Cambridge CB3 0WB, UK. Email address: l.c.g.rogers@statslab.cam.ac.uk
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Abstract

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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.

Keywords

Optimal investmentoptimal stoppingBrownian motion

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 62L15: Optimal stopping
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 898 - 909
Copyright
© Applied Probability Trust 

References

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