The Dynamic Programming Equation for the Problem of Optimal Investment Under Capital Gains Taxes

Imen Ben Tahar (), Nizar Touzi and Mete Soner ()
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Imen Ben Tahar: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Nizar Touzi: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Mete Soner: D-MATH - Department of Mathematics [ETH Zurich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

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Abstract: This paper considers an extension of the Merton optimal investment problem to the case where the risky asset is subject to transaction costs and capital gains taxes. We derive the dynamic programming equation in the sense of constrained viscosity solutions. We next introduce a family of functions $(V_\varepsilon)_{\varepsilon>0}$, which converges to our value function uniformly on compact subsets, and which is characterized as the unique constrained viscosity solution of an approximation of our dynamic programming equation.

Keywords: optimal consumption and investment in continuous time; transaction costs; capital gains taxes; viscosity solutions (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (9)

Published in SIAM Journal on Control and Optimization, 2007, 46 (5), pp.1779-1801. ⟨10.1137/050646044⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00703103

DOI: 10.1137/050646044

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