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

28 Pages Posted: 13 Dec 2013 Last revised: 24 Jul 2014

See all articles by Xinfu Chen

Xinfu Chen

Independent

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Date Written: December 12, 2013

Abstract

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

Suggested Citation

Chen, Xinfu and Dai, Min, Asymptotics for Merton Problem with Capital Gain Taxes and Small Interest Rate (December 12, 2013). Available at SSRN: https://ssrn.com/abstract=2175419 or http://dx.doi.org/10.2139/ssrn.2175419

Xinfu Chen

Independent ( email )

No Address Available
United States

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

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