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

Imen Ben Tahar, H. Mete Soner, Nizar Touzi

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14 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 languageEnglish (US)
Pages (from-to)1779-1801
Number of pages23
JournalSIAM Journal on Control and Optimization
Volume46
Issue number5
DOIs
StatePublished - 2007

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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