Economy – Quantitative Finance – Portfolio Management
Scientific paper
2008-06-25
Annals of Applied Probability 2008, Vol. 18, No. 5, 1681-1705
Economy
Quantitative Finance
Portfolio Management
Published in at http://dx.doi.org/10.1214/07-AAP511 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/07-AAP511
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.
Henderson Vicky
Hobson David
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