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

Soner, Halil Mete; Touzi, Nizar; Ben Tahar, Imen (2007), The Dynamic Programming Equation for the Problem of Optimal Investment Under Capital Gains Taxes, SIAM Journal on Control and Optimization, 46, 5, p. 1779–1801. http://dx.doi.org/10.1137/050646044

Type
Article accepté pour publication ou publié
Date
2007
Journal name
SIAM Journal on Control and Optimization
Volume
46
Number
5
Publisher
Society for Industrial and Applied Mathematics
Pages
1779–1801
Publication identifier
Metadata
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Author(s)
Soner, Halil Mete

Touzi, Nizar
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ben Tahar, Imen
Abstract (EN)
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.
Subjects / Keywords
viscosity solutions; capital gains taxes; transaction costs; optimal consumption and investment in continuous time
JEL
D23 - Organizational Behavior; Transaction Costs; Property Rights