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Optimal investment strategy to minimize occupation time

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Erhan Bayraktar & Virginia R. Young

Authors
  1. Erhan Bayraktar
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  2. Virginia R. Young
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Correspondence to Erhan Bayraktar.

Additional information

E. Bayraktar is supported in part by the National Science Foundation.

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Bayraktar, E., Young, V.R. Optimal investment strategy to minimize occupation time. Ann Oper Res 176, 389–408 (2010). https://doi.org/10.1007/s10479-008-0467-2

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  • DOI: https://doi.org/10.1007/s10479-008-0467-2

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