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Continuous time optimal stochastic growth: local martingales, transversality and existence

Foldes, Lucien (2004) Continuous time optimal stochastic growth: local martingales, transversality and existence. 479. Financial Markets Group, London School of Economics and Political Science, London, UK.

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Abstract

This lengthy paper extends the author's work on optimal planning of consumption versus capital accumulation to stochastic versions of traditional continuous-time one­sector growth models. Risk is assumed to be exogenous but is otherwise specified in a very general form. An optimal plan is characterised by means of local martingale conditions for shadow prices and transversality conditions at infinity. The definitions of these conditions involve sequences of random stopping times, and various choices of these times which are of economic interest are considered. For example, assumptions are given which allow the stopping times to be chosen as clock times, so that the local martingale is a true martingale and the expected capital value tends to zero as clock time tends to infinity. The possibility of making random time changes so as to replace ­local by true martingale conditions for an optimum is also considered. Separately, conditions for the existence of an optimum are obtained.

Item Type: Monograph (Discussion Paper)
Official URL: http://fmg.lse.ac.uk
Additional Information: © 2004 the author
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Sets: Research centres and groups > Financial Markets Group (FMG)
Collections > Economists Online
Departments > Economics
Collections > LSE Financial Markets Group (FMG) Working Papers
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: 479
Date Deposited: 29 May 2008 09:36
URL: http://eprints.lse.ac.uk/5141/

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