Investment, Income, and Incompleteness

30 Pages Posted: 16 Feb 2009

See all articles by Björn Bick

Björn Bick

Goethe University Frankfurt

Holger Kraft

Goethe University Frankfurt

Claus Munk

Copenhagen Business School

Multiple version iconThere are 2 versions of this paper

Date Written: February 15, 2009


The utility-maximizing consumption and investment strategy of an individual investor receiving an unspanned labor income stream seems impossible to find in closed form and very difficult to find using numerical solution techniques. We suggest an easy procedure for finding a specific, simple, and admissible consumption and investment strategy, which is near-optimal in the sense that the wealth-equivalent loss compared to the unknown optimal strategy is very small. We first explain and implement the strategy in a simple setting with constant interest rates, a single risky asset, and an exogenously given income stream, but we also show that the success of the strategy is robust to changes in parameter values, to the introduction of stochastic interest rates, and to endogenous labor supply decisions.

Keywords: Optimal consumption and investment, labor income, incomplete markets, artificially completed markets, welfare loss

JEL Classification: G11

Suggested Citation

Bick, Björn and Kraft, Holger and Munk, Claus, Investment, Income, and Incompleteness (February 15, 2009). Available at SSRN: or

Björn Bick

Goethe University Frankfurt ( email )

Grüneburgplatz 1
Frankfurt am Main, 60323

Holger Kraft

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323

Claus Munk (Contact Author)

Copenhagen Business School ( email )

Department of Finance
Solbjerg Plads 3
Frederiksberg, DK-2000


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