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An Introduction to Dynamic Programming

Published online by Cambridge University Press:  11 August 2014

Brian Gluss
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Extract

Dynamic programming, a mathematical field that has grown up in the past few years, is recognized in the U.S.A. as an important new research tool. However, in other countries, little interest has as yet been taken in the subject, nor has much research been performed. The objective of this paper is to give an expository introduction to the field, and give an indication of the variety of actual and possible areas of application, including actuarial theory.

In the last decade a large amount of research has been performed by a small body of mathematicians, most of them members of the staff of the RAND Corporation, in the field of multi-stage decision processes, and during this time the theory and practice of the art have experienced great advances. The leading force in these advances has been Richard Bellman, whose contributions to the subject, which he has entitled Dynamic Programming [1], have had effects not only in immediate fields of application but also in general mathematical theory; for example, the calculus of variations (see chapter IX of [1]), and linear programming (chapter VI).

Type
Research Article
Information
Journal of the Staple Inn Actuarial Society , Volume 16 , Issue 4 , July 1961 , pp. 261 - 274
Copyright
Copyright © Institute of Actuaries Students' Society 1961

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References

REFERENCES

[1] Bellman, R. (1957). Dynamic Programming. Princeton University Press. (The reader should perhaps be cautioned that, as is to be expected for any important mathematical first edition, there are a certain number of slight errors.)Google Scholar
[2] Gluss, B. (1960). ‘An optimal inventory solution for some specific demand distributions’. Naval Research Logistics Quarterly, 7, no. 1, 45–48.CrossRefGoogle Scholar
[3] Levy, J. (1959). Further notes on the loss resulting from the use of incorrect data in computing an optimal policy. Naval Research Logistics Quarterly, 6, no. 1, 25–31.Google Scholar
[4] Bellman, R. & Kalaba, R. (1958). On communication processes involving learning and random duration. RAND Research Memorandum P-1194.Google Scholar
[5] Bellman, R. (1961). Adaptive Control; A Guided Tour. Princeton University Press.Google Scholar
[6] Kalaba, R. (1959). Some aspects of adaptive control processes. RAND Research Memorandum P-1809.Google Scholar
[7] Johnson, S. M. (1956). Optimal sequential testing. RAND Research Memorandum RM-1652.Google Scholar
[8] Gluss, B. (1959). An optimum policy for detecting a fault in a complex system. Operations Research, 7, no. 4, 467–477.Google Scholar
[9] Firstman, S. I. & Gluss, B. (1960). Optimum search routines for automatic fault location. Operations Research, 8, no. 4, 512–523.Google Scholar
[10] Bellman, R. & Kalaba, R. (1957). On the role of dynamic programming in statistical communication theory. IRE Transactions of the Professional Group on Information Theory, vol. IT-3, no. 3.Google Scholar
[11] Kalaba, R. & Juncosa, M. L. (1956). Optimal design and utilization of communication networks. RAND Research Memorandum P-782.Google Scholar
[12] Kalaba, R. (1959). On some communication network problems. RAND Research Memorandum P-1325.Google Scholar