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Growth and optimal intertemporal allocation of risks. (English) Zbl 1011.91504

The author attempts to provide an informal economic interpretation of the Hamiltonian systems arising in problems of stochastic optimal control. For a rigorous discussion of the analytical framework the reader is referred to the author’s paper [J. Math. Anal. Appl. 44, 384-404 (1973; Zbl 0276.93060)]. The interpretation of the dual variables as appropriate shadow prices is less transparent than in the deterministic Pontryagin formulation. Given the overwhelming importance of optimization problems in economics, the basic techniques are likely to be helpful in understanding the problems of intertemporal allocation under uncertainty, particularly the questions related to risk bearing, information processing and decentralization of decision making through prices.

MSC:

91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 0276.93060
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References:

[1] Arrow, K. J.; Kurz, M., Public investment, the rate of return, and optimal fiscal policy (1970), Johns Hopkins Press: Johns Hopkins Press Baltimore
[2] Bismut, J. M., Analyse Convexe et Probabilités, (Doctoral Dissertation (1973), Faculté des Sciences de Paris)
[3] Bismut, J. M., Conjugate convex fonctions in optimal stochastic control, J. Math. and Appl., 44, 384-404 (November 1973)
[4] Burmeister, E.; Dobell, A. R., (Mathematical Theories of Economic Growth (1970), Macmillan: Macmillan New York) · Zbl 0238.90009
[5] Dorfman, R., (An Economic Interpretation of Optimal Control Theory (December 1969), A.E.R.), 817-831
[6] Fama, E., Efficient capital markets, J. Finance, 383-417 (May 1970)
[7] Merton, R. C., Optimum consumption and portfolio rules in a continuous-time model, J. Econ. Theory, 3, 373-413 (1971) · Zbl 1011.91502
[8] Samuelson, P. A., Some Aspects of the Pure Theory of Capital, Quart. J. Econ., LI, 469-496 (May, 1937)
[9] Sharpe, W. F., Portfolio theory and capital markets (1970), McGraw-Hill: McGraw-Hill New York
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