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R&D projects analyzed by semimartingale methods

Published online by Cambridge University Press:  14 July 2016

Knut K. Aase
Knut K. Aase*
Affiliation:
Norwegian School of Economics and Business Administration
*
∗Postal address: Department of Insurance, Norwegian School of Economics and Business Adminstration, 5035 Sandviken, Norway.
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Abstract

In this article we examine R&D projects where the project status changes according to a general dynamic stochastic equation. This allows for both continuous and jump behavior of the project status. The time parameter is continuous. The decision variable includes a non-stationary resource expenditure strategy and a stopping policy which determines when the project should be terminated. Characterization of stationary policies becomes straightforward in the present setting. A non-linear equation is determined for the expected discounted return from the project. This equation, which is of a very general nature, has been considered in certain special cases, where it becomes manageable. The examples include situations where the project status changes according to a compound Poisson process, a geometric Brownian motion, and a Brownian motion with drift. In those cases we demonstrate how the exact solution can be obtained and the optimal policy found.

Keywords

STOCHASTIC DIFFERENTIAL EQUATIONSOPTIMAL STOPPINGCONTROL OF A SEMIMARTINGALEITO–MEYER'S FORMULACOMPOUND POISSON PROCESSDIFFUSIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 288 - 299
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Part of the research was carried out when the author was visiting the Department of Statistics, University of California, Berkeley.

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