Merton Problem with Taxes: Characterization, computation and Approximation

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: We formulate a computationally tractable extension of the classical Merton optimal consumptioninvestment problem to include the capital gains taxes. This is the continuous-time version of the model introduced by Dammon, Spatt, and Zhang [Rev. Financ. Stud., 14 (2001), pp. 583-616]. In this model the tax basis is computed as the average cost of the stocks in the investor's portfolio. This average rule introduces only one additional state variable, namely the tax basis. Since the other tax rules such as the first in first out rule require the knowledge of all past transactions, the average model is computationally much easier. We emphasize the linear taxation rule, which allows for tax credits when capital gains losses are experienced. In this context wash sales are optimal, and we prove it rigorously. Our main contributions are a first order explicit approximation of the value function of the problem and a unique characterization by means of the corresponding dynamic programming equation. The latter characterization builds on technical results isolated in the accompanying paper [I. Ben Tahar, H. M. Soner, and N. Touzi, SIAM J. Control Optim., 46 (2007), pp. 1779-1801]. We also suggest a numerical computation technique based on a combination of finite differences and the Howard iteration algorithm. Finally, we provide some numerical results on the welfare consequences of taxes and the quality of the first order approximation.

Keywords: optimal consumption and investment in continuous time; transaction costs; capital gains taxes; finite differences (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (9)

Published in SIAM Journal on Financial Mathematics, 2010, 1, pp.366-395. ⟨10.1137/080742178⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00703102

DOI: 10.1137/080742178

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