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Optimal lifetime consumption and investment under a drawdown constraint

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Abstract

We consider the infinite-horizon optimal consumption-investment problem under a drawdown constraint, i.e., when the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the with constant coefficients. For a general class of utility functions, we provide the value function in explicit form and derive closed-form expressions for the optimal consumption and investment strategy.

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Authors and Affiliations

  1. CEREMADE & CREST, Paris, France

    Romuald Elie

  2. Centre de Mathématiques Appliquées, Ecole Polytechnique Paris, Paris, France

    Nizar Touzi

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  1. Romuald Elie
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  2. Nizar Touzi
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Correspondence to Romuald Elie.

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Elie, R., Touzi, N. Optimal lifetime consumption and investment under a drawdown constraint. Finance Stoch 12, 299–330 (2008). https://doi.org/10.1007/s00780-008-0066-8

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  • DOI: https://doi.org/10.1007/s00780-008-0066-8

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