文档介绍：A stochastic control model for individual
asset-liability management∗
Sachi Purcal
School of Actuarial Studies
University of New South Wales†
March 2003
Abstract
In the tradition of Merton (1969, 1971) we seek to describe the opti-
mal behaviour of an individual through his lifetime. Our model is based on
Richard (1975), which includes optimal insurance and annuity demand. We
extend that work by modelling labour e as a stochastic process, explic-
itly recognising the market pleteness posed by salaries, as opposed to
the deterministic e flows assumed in Richard. A closed-form solution
is not available for this finite horizon problem. We adopt the Markov chain
technique of Kushner & Dupuis (2001) to solve the model. Our solution
provides support for hump shaped consumption, age-phased investment and
optimal life insurance rules related to e levels.
Keywords: Asset-liability modelling, optimal portfolio selection, finan-
cial planning, life insurance, annuities, stochastic control.
Journal of Economic Literature Classification Numbers: C63, D91, G11,
G22, J26.
∗I would like to thank John Piggott for ments and discussion and Geoffrey
Kingston for guidance with the literature. Russell Standish and Duraid Madina were very helpful
in assistance with HPC matters, as was Patrick Young in puting matters. Part of this
work was done while the author was visiting the Universit¨at Karlsruhe (TH), and I thank Chris-
tian Hipp for his hospitality. Financial support from the Economic and Social Research Institute
(Tokyo, Japan) and the Australia Research Council is gratefully acknowledged.
†Sydney, 2052, Australia. Telephone: +61 (2) 9385–3566. Fax: +61 (2) 9385–1883. E-mail:
s.******@.
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1 Introduction 2
1 Introduction
For the vast majority of workers human capital is an extremely po-
nent of their total wealth. The e process is thus highly influential on individ-
ual decision making. The Richard (1975) model assumes e