Asymptotics for Merton Problem with Capital Gain Taxes and Small Interest Rate

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"