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Optimal reserves growth under a Wiener process

Published online by Cambridge University Press:  14 July 2016

W. F. Foster
W. F. Foster*
Affiliation:
University of Melbourne
*
*Address from December 1975: 137 Hampden Road, Hobart, Tasmania 7000, Australia.
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Abstract

This paper considers a body whose funds accumulate according to a Wiener Process that has parameters which can be controlled at any stage. The process is bounded above by a level at which dividends (or savings) are set aside, and it is bounded below by a level at which a ‘rescue’ policy is invoked to avoid insolvency. Taking long-term dividend maximisation as the optimality criterion, first passage times are used to derive a general first order differential equation for the optimal control of the system at any reserves level, and this equation is solved fully for a certain class of problems. Examples are given of insurance and investment applications.

Keywords

BOUNDED WIENER PROCESSDRIFTDISPERSIONRESCUE POLICYDIVIDENDSFIRST PASSAGE TIMESOPTIMISATIONINVESTMENTINSURANCEREINSURANCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 457 - 465
Copyright
Copyright © Applied Probability Trust 1975 

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References

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