Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies
44 Pages Posted: 11 Mar 2009 Last revised: 17 Apr 2012
Date Written: April 17, 2012
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: Suggested Citation