Analysis of an optimal stopping problem arising from hedge fund investing

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Chen, Xinfu¹  Saunders, David²  Chadam, John¹ 

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON, Canada

关键词: Optimal stopping;    Free boundary problems;    Mathematical finance;    Variational inequalities;    Stefan problem;   

DOI  :  10.1016/j.jmaa.2019.123559

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free