Abstract
This paper makes endogenous the probability assignment of an economic agent in a familiar two-period finance model by basing the probability assignment upon available information. The Principle of Maximum Entropy (PME) reduces an economic decision made under uncertainty to a decision made under risk. The PME accomplishes this because the necessary conditions for a probability distribution to achieve maximum entropy, given certain information, are equivalent to the conditions characterizing a distribution for which the information forms a sufficient statistic of fixed dimension.
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References
DeGroot, M.H.: 1970, Optimal Statistical Decisions, McGraw-Hill, New York.
Fraser, D.A.S.: 1963, ‘On Sufficiency and the Exponential Family’, Journal of the American Statistical Association 58, 641–647.
Hakansson, N.H.: 1978, ‘Welfare Aspects of Options and Supershares’, Journal of Finance 33, 759–776.
Hakansson, N.H.: 1982a, ‘To Pay or Not to Pay Dividend’, Journal of Finance 37, 415–428.
Hakansson, N.H.: 1982b, ‘Changes in the Financial Market: Welfare and Price Effects and the Basic Theorems of Value Conservation’, Journal of Finance 37, 977–1004.
Hakansson, N.H., J.G. Kunkel, and J.A. Ohlson: 1982, ‘Sufficient and Necessary Conditions for Information to Have Social Value in Pure Exchange’, Journal of Finance 37, 1169–1181.
Jaynes, E.T.: 1968, ‘Prior Probabilities’, IEEE Transactions on Systems Science and Cybernetics SSC-4, 227–241.
Jaynes, E.T.: 1978, ‘Where Do We Stand on Maximum Entropy?’ in The Maximum Entropy Formalism, R. Levine and M. Tribus (eds.), MIT Press.
Jaynes, E.T.: 1983, ‘Brandeis Lectures, 1962’, in Papers on Probability, Statistics, and Statistical Physics, R.D. Rosenkrantz (ed.), Reidel Publishing, Dordrecht.
Kaiman, R.E.: 1976, ‘Algebraic Aspects of the Generalized Inverse of a Rectangular Matrix’, in Generalized Inverses and Applications, M.Z. Nashed (ed.), Academic Press, New York.
Keynes, J.M.: 1921, A Treatise on Probability, MacMillan, London.
Knight, F.H.: 1921, Risk, Uncertainty and Profit, Houghton Mifflin. Reprinted by University of Chicago Press, Chicago, 1971.
LeRoy, S.F. and L.D. Singell, Jr.: 1987, ‘Knight on Risk and Uncertainty’, Journal of Political Economy 95, 394–406.
Noble, B. and J.W. Daniel: 1977, Applied Linear Algebra, 2nd edition, Prentice-Hall, Englewood Cliffs, New Jersey.
Savage, L.J.: 1954, The Foundations of Statistics. Reprinted by Dover, New York, 1972.
Shannon, C.E.: 1948, ‘The Mathematical Theory of Communication’, Bell System Technical Journal. Reprinted in C. Shannon and W. Weaver: 1949, The Mathematical Theory of Communication, University of Illinois Press, Urbana.
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© 1991 Springer Science+Business Media Dordrecht
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Grandy, C. (1991). The Principle of Maximum Entropy and the Difference between Risk and Uncertainty. In: Grandy, W.T., Schick, L.H. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3460-6_4
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DOI: https://doi.org/10.1007/978-94-011-3460-6_4
Publisher Name: Springer, Dordrecht
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