Analysis of an optimal stopping problem arising from hedge fund investing. (English) Zbl 1427.91270
Summary: 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.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
Keywords:
optimal stopping; free boundary problems; mathematical finance; variational inequalities; Stefan problemReferences:
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