Consumption in Incomplete Markets

30 Pages Posted: 20 Mar 2014 Last revised: 17 Jun 2018

See all articles by Paolo Guasoni

Paolo Guasoni

Boston University - Department of Mathematics and Statistics; Dublin City University - School of Mathematical Sciences; University of Bologna - Department of Statistics

Gu Wang

Worcester Polytechnic Institute

Date Written: November 14, 2016

Abstract

We develop a method to fi nd approximate solutions, and their accuracy, to consumption-investment problems with isoelastic preferences and in nite horizon, in incomplete markets where state variables follow a multivariate di ffusion. We construct upper and lower contractions, fi ctitious complete markets in which state variables are fully hedgeable, but their dynamics is distorted. Such contractions yield pointwise upper and lower bounds for both the value function and the optimal consumption of the original incomplete market, and their optimal policies are explicit in typical models. Approximate consumption-investment policies coincide with the optimal one if the market is complete or utility logarithmic. An application to an incomplete market with stochastic excess returns, risk premia, and volatilities, shows that the welfare loss of the proposed approximations is equivalent to a capital loss of less than 3% for realistic parameter values.

Keywords: portfolio choice, consumption, incomplete markets, power utility

JEL Classification: G11, G12

Suggested Citation

Guasoni, Paolo and Guasoni, Paolo and Wang, Gu, Consumption in Incomplete Markets (November 14, 2016). Available at SSRN: https://ssrn.com/abstract=2411236 or http://dx.doi.org/10.2139/ssrn.2411236

Paolo Guasoni (Contact Author)

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

Gu Wang

Worcester Polytechnic Institute ( email )

100 Institute Road
Worcester, MA 01609
United States

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