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Stochastic Models for Actuarial Use: The Equilibrium Modelling of Local Markets

Published online by Cambridge University Press:  09 August 2013

Robert J. Thomson  and
Dmitri V. Gott
Robert J. Thomson
Affiliation:
School of Statistics and Actuarial Science, University of the Witwatersrand, Johannesburg
Dmitri V. Gott
Affiliation:
School of Statistics and Actuarial Science, University of the Witwatersrand, Johannesburg
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Abstract

In this paper, a long-term equilibrium model of a local market is developed. Subject to minor qualifications, the model is arbitrage-free. The variables modelled are the prices of risk-free zero-coupon bonds – both index-linked and conventional – and of equities, as well as the inflation rate. The model is developed in discrete (nominally annual) time, but allowance is made for processes in continuous time subject to continuous rebalancing. It is based on a model of the market portfolio comprising all the above-mentioned asset categories. The risk-free asset is taken to be the one-year index-linked bond. It is assumed that, conditionally upon information at the beginning of a year, market participants have homogeneous expectations with regard to the forthcoming year and make their decisions in mean-variance space. For the purposes of illustration, a descriptive version of the model is developed with reference to UK data. The parameters produced by that process may be used to inform the determination of those required for the use of the model as a predictive model. Illustrative results of simulations of the model are given.

Keywords

Stochastic investment modelsactuarial modelsequilibrium modelsno-arbitrage modelsUnited Kingdom
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 339 - 370
Copyright
Copyright © International Actuarial Association 2009

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