Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T17:01:00.755Z Has data issue: false hasContentIssue false
  • English
  • Français

A diffusion process model for the optimal investment strategies of an R & D project

Published online by Cambridge University Press:  14 July 2016

Dror Zuckerman
Dror Zuckerman*
Affiliation:
The Hebrew University of Jerusalem
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article we examine an R & D project in which the project status changes according to a diffusion process. The decision variables include a resource expenditure strategy and a stopping policy which determines when the project should be terminated. The drift and the diffusion parameters of the project status process are assumed to be functions of the resource expenditure rate.

The terminal reward from the project is a non-decreasing function of the project status. Our purpose is to select optimal investment strategies under the discounted return criterion.

The value of the project is shown to be a solution of a second order, non-linear differential equation. Finally, we derive the optimal investment strategies for an R & D project in which the project status changes according to a non-homogeneous compound Poisson process by using diffusion approximation.

Keywords

R & D PROJECTDIFFUSION PROCESSOPTIMAL CONTROLSTATIONARY POLICIESSTOPPING TIMERESOURCE EXPENDITURE STRATEGYNON-HOMOGENEOUS POISSON PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 646 - 653
Copyright
Copyright © Applied Probability Trust 1980 

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

Aldrich, C. and Morton, T. E. (1975) Optimal funding paths for a class of risky R & D projects. Management Sci. 21, 491–500.Google Scholar
Deshmukh, S. D. and Chikte, S. D. (1977) Dynamic investment strategies for a risky R & D project. J. Appl. Prob. 14, 144–152.Google Scholar
Kamien, M. I. and Schwartz, N. L. (1971) Expenditure patterns for risky R & D projects. J. Appl. Prob. 8, 60–73.CrossRefGoogle Scholar
Kamien, M. I. and Schwartz, N. L. (1974) Risky R & D with rivalry. Ann. Econ. Soc. Measurement 3, 266–277.Google Scholar
Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
Laska, E., Meisner, M. and Siegel, C. (1972) Contributions to the theory of optimal resource allocation. J. Appl. Prob. 9, 337–359.CrossRefGoogle Scholar
Lucas, R. E. (1971) Optimal management of an R & D project. Management Sci. 17, 679–697.CrossRefGoogle Scholar
Mandl, P. (1968) Analytical Treatment of One-Dimensional Markov Processes. Springer-Verlag, New York.Google Scholar
Pliska, S. R. (1973a) Single person controlled diffusions with discounted costs. J. Optimization Theory Appl. 12, 248–255.Google Scholar
Pliska, S. R. (1973b) Multiperson controlled diffusions. SIAM J. Control 11, 563–586.CrossRefGoogle Scholar