Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T16:38:08.142Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bather, J. A. (1966) A continuous time inventory model. J. Appl. Prob. 3, 538–549.Google Scholar
Bather, J. A. (1968) A diffusion model for the control of a dam. J. Appl. Prob. 5, 55–71.Google Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
Dayananda, P. W. A. (1970) Optimal reinsurance. J. Appl. Prob. 7, 134–156.Google Scholar
Foster, W. F. (1972) Optimal Insurance Processes. M. Sc. thesis, University of Melbourne.Google Scholar