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State-Dependent Utility

Part of: Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Jaime A. Londoño
Jaime A. Londoño*
Affiliation:
Universidad Nacional de Colombia
*
∗Postal address: Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá. Email address: jaime.a.londono@gmail.com
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Abstract

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We propose a new approach to utilities in (state) complete markets that is consistent with state-dependent utilities. Full solutions of the optimal consumption and portfolio problem are obtained in a very general setting which includes several functional forms for utilities used in the current literature, and consider general restrictions on allowable wealths. As a secondary result, we obtain a suitable representation for straightforward numerical computations of the optimal consumption and investment strategies. In our model, utilities reflect the level of consumption satisfaction of flows of cash in future times as they are (uniquely) valued by the market when the economic agents are making their consumption and investment decisions. The theoretical framework used for the model is the one proposed in Londoño (2008). We develop the martingale methodology for the solution of the problem of optimal consumption and investment in this setting.

Keywords

State-dependent utilitystochastic flowoptimal consumption and investment

MSC classification

Secondary: 91B16: Utility theory
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 1 , March 2009 , pp. 55 - 70
Copyright
Copyright © Applied Probability Trust 2009 

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