Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies

44 Pages Posted: 11 Mar 2009 Last revised: 17 Apr 2012

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: April 17, 2012

Abstract

Utility-maximizing consumption and investment strategies in closed form are unknown for realistic settings involving portfolio constraints, incomplete markets, and potentially a high number of state variables. Standard numerical methods are hard to implement in such cases. We propose a numerical procedure that combines the abstract idea of artificial, unconstrained complete markets, well-known closed-form solutions in affine or quadratic return models, straightforward Monte Carlo simulation, and a standard iterative optimization routine. Our method provides an upper bound on the wealth-equivalent loss compared to the unknown optimal strategy, and it facilitates our understanding of the economic forces at play by building on closed-form expressions for the strategies considered. We illustrate and test our method on the life-cycle problem of an individual who receives unspanned labor income and cannot borrow or short-sell. The upper loss bound is small and our method performs well in comparison with two existing methods.

Keywords: Optimal consumption and investment, numerical solution, labor income, incomplete markets, artificially unconstrained markets, welfare loss

JEL Classification: G11, C63

Suggested Citation

Bick, Björn and Kraft, Holger and Munk, Claus, Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies (April 17, 2012). Available at SSRN: https://ssrn.com/abstract=1357339 or http://dx.doi.org/10.2139/ssrn.1357339

Björn Bick

Goethe University Frankfurt ( email )

Grüneburgplatz 1
Frankfurt am Main, 60323
Germany

Holger Kraft

Goethe University Frankfurt ( email )

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

Claus Munk (Contact Author)

Copenhagen Business School ( email )

Department of Finance
Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark

HOME PAGE: http://sites.google.com/view/clausmunk/home

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