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Analysis of an Optimal Stopping Problem Arising from Hedge Fund Investing

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HedgeFundFeesAmerican_V12.pdf (477.37 KB)

Date

2020

Authors

Chen, Xinfu
Saunders, David
Chadam, John

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

We analyze the optimal withdrawal time for an investor in a hedge fund with a first-loss or shared-loss fee structure, given as the solution of an optimal stopping problem on the fund's assets with a piecewise linear payoff function. Assuming that the underlying follows a geometric Brownian motion, we present a complete solution of the problem in the infinite horizon case, showing that the continuation region is a finite interval, and that the smooth-fit condition may fail to hold at one of the endpoints. In the finite horizon case, we show the existence of a pair of optimal exercise boundaries and analyze their properties, including smoothness and convexity.

Description

The final publication is available at Elsevier via https://doi.org/10.1016/j.jmaa.2019.123559. © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

optimal stopping, free boundary problems, mathematical finance, variational inequalities, Stefan problem

LC Keywords

Citation

URI

https://doi.org/10.1016/j.jmaa.2019.123559
 http://hdl.handle.net/10012/20091

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Waterloo Research