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Risks 2014, 2(2), 171-194; doi:10.3390/risks2020171

Optimal Consumption and Investment with Labor Income and European/American Capital Guarantee

ATP (Danish Labour Market Supplementary Pension Scheme), Kongens Vænge 8, 3400 Hillerød, Denmark, and, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5,2100 Copenhagen Ø, Denmark
Received: 10 March 2014 / Revised: 5 May 2014 / Accepted: 7 May 2014 / Published: 16 May 2014
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Abstract

We present the optimal consumption and investment strategy for an investor, endowed with labor income, searching to maximize utility from consumption and terminal wealth when facing a binding capital constraint of a European (constraint on terminal wealth) or an American (constraint on the wealth process) type. In both cases, the optimal strategy is proven to be of the option-based portfolio insurance type. The optimal strategy combines a long position in the optimal unrestricted allocation with a put option. In the American case, where the investor is restricted to fulfill a capital guarantee at every intermediate time point over the interval of optimization, we prove that the investor optimally changes his budget constraint for the unrestricted allocation whenever the constraint is active. The strategy is explained in a step-by-step manner, and numerical illustrations are presented in order to support intuition and to compare the restricted optimal strategy with the unrestricted optimal counterpart. View Full-Text
Keywords: stochastic control; martingale method; option-based portfolio insurance; American put option; human capital; borrowing constraint; CRRA utility stochastic control; martingale method; option-based portfolio insurance; American put option; human capital; borrowing constraint; CRRA utility
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Kronborg, M.T. Optimal Consumption and Investment with Labor Income and European/American Capital Guarantee. Risks 2014, 2, 171-194.

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