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October 2008 An explicit solution for an optimal stopping/optimal control problem which models an asset sale
Vicky Henderson, David Hobson
Ann. Appl. Probab. 18(5): 1681-1705 (October 2008). DOI: 10.1214/07-AAP511

Abstract

In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the decision over when to sell, the agent has to choose a control strategy which corresponds to a feasible wealth process.

We formulate this problem as one involving the choice of a stopping time and a martingale. We conjecture the form of the solution and verify that the candidate solution is equal to the value function.

The interesting features of the solution are that it is available in a very explicit form, that for some parameter values the optimal strategy is more sophisticated than might originally be expected, and that although the setup is based on continuous diffusions, the optimal martingale may involve a jump process.

One interpretation of the solution is that it is optimal for the risk-averse agent to gamble.

Citation

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Vicky Henderson. David Hobson. "An explicit solution for an optimal stopping/optimal control problem which models an asset sale." Ann. Appl. Probab. 18 (5) 1681 - 1705, October 2008. https://doi.org/10.1214/07-AAP511

Information

Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1165.60021
MathSciNet: MR2462545
Digital Object Identifier: 10.1214/07-AAP511

Subjects:
Primary: 60G40, 91A60
Secondary: 60G44, 91B28, 93E20

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 5 • October 2008
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