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Conditions for optimality in the infinite-horizon portfolio-cum-saving problem with semimartingale investments

By Lucien Foldes

Abstract

A model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time is formulated in which the vector process representing returns to investments is a general semimartingale. Methods of stochastic calculus and calculus of variations are used to obtain necessary and sufficient conditions for optimality involving martingale properties of the ‘shadow price’ processes associated with alternative portfolio-cum-saving plans. The relationship between such conditions and ‘portfolio equations’ is investigated. The results are applied to special cases where the returns process has stationary independent increments and the utility function has the ‘discounted relative risk aversion’ form

Topics: HG Finance, HB Economic Theory, QA Mathematics
Publisher: Financial Markets Group, London School of Economics and Political Science
Year: 1989
OAI identifier: oai:eprints.lse.ac.uk:5142
Provided by: LSE Research Online
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