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Stochastic control of geometric processes

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: Norwegian School of Economics and Business Administration, 5035 Bergen, Norway.
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Abstract

Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

Keywords

SEMIMARTINGALESSTOCHASTIC DIFFERENTIAL EQUATIONSDOLÉANS-DADE'S FORMULAGROWTH MODELSPORTFOLIO OPTIMIZATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 97 - 104
Copyright
Copyright © Applied Probability Trust 1987 

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References

[1]Aase, K. K. (1984) Optimum portfolio diversification in a general continuous-time model. Stoch. Proc. Appl. 18, 81–98.Google Scholar
[2]Aase, K. K. (1985) R&D projects analyzed by semi-martingale methods. J. Appl. Prob. 22, 288–299.Google Scholar
[3]Aase, K. K. (1986) Ruin problems and myopic portfolio optimization in continuous trading. Stoch. Proc. Appl. 21, 213–227.Google Scholar
[4]Aase, K. K. and Guttorp, P. (1984) Estimation of models for security prices. Technical report no. 52, Department of Statistics, University of Washington, Seattle.Google Scholar
[5]Aase, K. K. and Øksendal, B. (1986) Admissible investment strategies in continuous trading. Technical report No. 59, Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
[6]Benež, V. E. (1970) Existence of optimal strategies based on specified information, for a class of stochastic decision problems. SIAM J. Control 8, 179–184.Google Scholar
[7]Breiman, L. (1960) Investment policies for expanding business optimal in a long run sense. Naval Res. Logist. Quart. 7, 647–651.Google Scholar
[8]Bremaud, P. (1981) Point Processes and Queues. Martingale Dynamics. Springer-Verlag, New York.10.1007/978-1-4684-9477-8Google Scholar
[9]Elliott, R. J. (1982) Stochastic Calculus and Applications. Springer-Verlag, New York,Google Scholar
[10]Gihman, I. I. and Skorohod, A. V. (1979) Controlled Stochastic Processes. Springer-Verlag, Berlin10.1007/978-1-4612-6202-2Google Scholar
[11]Mossin, J. (1968) Optimal multiperiod portfolio policies. J. Business 41, 215–229.Google Scholar
[12]Thorp, E. O. (1971) Portfolio choice and the Kelly criterion. In Stochastic Optimization Models in Finance, ed. Ziemba, W. T. and Wickson, R. G., Academic Press, New York, 599–619.Google Scholar