By the classical separation theorem
, there exists a nonzero functional [x.sup.*] [member of] [Z.sup.*], such that [x.sup.*]([member of]b' + [lambda]b) [less than or equal to] [x.sup.*] c + [x.sup.*] k for all b' [member of] B, [lambda] [member of] R, andk [member of] K.
for Convex Sets." SIAM Review (1 July 1959): 95-98.
The separation theorem
is translated into a simple two sector Keynesian macroeconomic model.
While the Fisher separation theorem
uses standard macroeconomic terminology quite comfortably, it fails to consider the implications of these terms.
We show that imperfect hedging violates both the separation theorem and the full hedging theorem.
In such case the widely discussed separation theorem and the full hedging theorem do not hold.
As a consequence of the Separation Theorem
we recover, in a more general setting but which is also contained in , Ansari's Theorem.
In Chapter 4 the Fisher Separation Theorem
is proved under uncertainty in different cases.
Fisher Separation Theorem
: (14) The manager paid in stock options now that vest then makes decisions on corporate account that are independent of the manager's preferences for consumption now versus then; the decisions on corporate account are made to maximize the warrant value W(I).
They begin with convex analysis, discussing such aspects as separation theorems
for convex sets, differentiability of convex functions and the sub-differential, and a problem of linear programming.
Nikodem, "Strong convexity and separation theorems
," Aequationes Mathematicae, vol.
Part II, "Qualitative Economic Results," contains subsections dealing with stochastic dominance, risk-aversion measures, and separation theorems
. This part contains an old friend of many Journal of Risk and Insurance readers: a reprint of Pratt's "Risk Aversion in the Small and in the Large." Part III, "Static Portfolio Selection Models," contains articles on mean-variance and safety-first approaches, existence and diversification of optimal portfolio policies, and the effects of taxes on risk taking.