The dynamic programming equation for the problem of optimal investment under capital gains taxes

Imen Ben Tahar; H. Mete Soner; Nizar Touzi

doi:10.1137/050646044

The dynamic programming equation for the problem of optimal investment under capital gains taxes

Imen Ben Tahar, H. Mete Soner, Nizar Touzi

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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 _∈)_∈>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. In particular, this result justifies the numerical results reported in the accompanying paper [I. Ben Tahar, H. M. Soner, and N. Touzi (2005), Modeling Continuous-Time Financial Markets with Capital Gains Taxes, preprint, http://www.cmap.polytechnique.fr/̃touzi/bst06.pdf].

Original language	English (US)
Pages (from-to)	1779-1801
Number of pages	23
Journal	SIAM Journal on Control and Optimization
Volume	46
Issue number	5
DOIs	https://doi.org/10.1137/050646044
State	Published - 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics

Keywords

Capital gains taxes
Optimal consumption and investment in continuous time
Transaction costs
Viscosity solutions

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10.1137/050646044

Cite this

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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 ∈)∈>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. In particular, this result justifies the numerical results reported in the accompanying paper [I. Ben Tahar, H. M. Soner, and N. Touzi (2005), Modeling Continuous-Time Financial Markets with Capital Gains Taxes, preprint, http://www.cmap.polytechnique.fr{\~/}touzi/bst06.pdf].",

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AU - Touzi, Nizar

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AB - 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 ∈)∈>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. In particular, this result justifies the numerical results reported in the accompanying paper [I. Ben Tahar, H. M. Soner, and N. Touzi (2005), Modeling Continuous-Time Financial Markets with Capital Gains Taxes, preprint, http://www.cmap.polytechnique.fr/̃touzi/bst06.pdf].

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The dynamic programming equation for the problem of optimal investment under capital gains taxes

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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