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Optimal lifetime consumption and investment under a drawdown constraint

Touzi, Nizar; Elie, Romuald (2008), Optimal lifetime consumption and investment under a drawdown constraint, Finance and Stochastics, 12, 3, p. 299-330. http://dx.doi.org/10.1007/s00780-008-0066-8

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Type
Article accepté pour publication ou publié
Date
2008
Journal name
Finance and Stochastics
Volume
12
Number
3
Publisher
Springer
Pages
299-330
Publication identifier
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Author(s)
Touzi, Nizar
Elie, Romuald
Abstract (EN)
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.
Subjects / Keywords
Verification; Duality; Drawdown constraint; Portfolio allocation