Asymptotics for Merton Problem with Capital Gain Taxes and Small Interest Rate
28 Pages Posted: 13 Dec 2013 Last revised: 24 Jul 2014
Date Written: December 12, 2013
We consider the Merton problem with capital gain taxes. Since closed-form solutions are generally unavailable, we provide asymptotic expansions with small interest rate and other parameters, and then obtain an explicit investment and consumption strategy that effectively approximates the optimal strategy. The expansions also offer qualitative and quantitative insights about the effects of various parameters on the optimal strategy. Moreover, we find that the optimal tax-deflated fraction of initial wealth in the risky asset is higher than the "Merton line".
Keywords: Optimal investment and consumption, Capital gain tax, Merton problem, Continuous-time, Asymptotic expansion
JEL Classification: G11, H24, K34, D91
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