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An explicit solution for an optimal stopping/optimal control problem which models an asset sale
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Henderson, Vicky and Hobson, David (David G.). (2008) An explicit solution for an optimal stopping/optimal control problem which models an asset sale. Annals of Applied Probability, Vol.18 (No.5). pp. 16811705. ISSN 10505164
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Official URL: http://dx.doi.org/10.1214/07AAP511
Abstract
In this article we study an optimal stopping/optimal control problem which models the decision facing a askaverse 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 riskaverse agent to gamble.
Item Type:  Journal Article  

Subjects:  H Social Sciences > HG Finance Q Science > QA Mathematics 

Divisions:  Faculty of Science > Statistics  
Library of Congress Subject Headings (LCSH):  Optimal stopping (Mathematical statistics), Control theory, Mathematical optimization, Utility theory, Capital market  Mathematical models, Local times (Stochastic processes)  
Journal or Publication Title:  Annals of Applied Probability  
Publisher:  Institute of Mathematical Statistics  
ISSN:  10505164  
Official Date:  October 2008  
Dates: 


Volume:  Vol.18  
Number:  No.5  
Number of Pages:  25  
Page Range:  pp. 16811705  
Identification Number:  10.1214/07AAP511  
Status:  Peer Reviewed  
Publication Status:  Published  
Funder:  Engineering and Physical Sciences Research Council (EPSRC)  
References:  [1] DIXIT, A. K. and PINDYCK, R. S. (1994). Investment under Uncertainty. Princeton Univ. 

URI:  http://wrap.warwick.ac.uk/id/eprint/29106 
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