Annals of Operations Research

, Volume 176, Issue 1, pp 389–408 | Cite as

Optimal investment strategy to minimize occupation time

  • Erhan Bayraktar
  • Virginia R. Young


We find the optimal investment strategy to minimize the expected time that an individual’s wealth stays below zero, the so-called occupation time. The individual consumes at a constant rate and invests in a Black-Scholes financial market consisting of one riskless and one risky asset, with the risky asset’s price process following a geometric Brownian motion. We also consider an extension of this problem by penalizing the occupation time for the degree to which wealth is negative.


Occupation time Optimal investment Stochastic control Free-boundary problem 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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