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The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The statement was first proven by Claude Berge in 1959. [1] The theorem is primarily used in mathematical economics and optimal control.
However, there is no hard and fast definition as to what is classified as "long" or "short" and mostly relies on the economic perspective being taken. Marshall's original introduction of long-run and short-run economics reflected the 'long-period method' that was a common analysis used by classical political economists.
"The Maximum Principle". Optimal Control Theory and Static Optimization in Economics. New York: Cambridge University Press. pp. 127– 168. ISBN 0-521-33158-7. Takayama, Akira (1985). "Developments of Optimal Control Theory and Its Applications". Mathematical Economics (2nd ed.). New York: Cambridge University Press. pp. 600– 719.
The optimal control can be derived using Pontryagin's maximum principle (a necessary condition also known as Pontryagin's minimum principle or simply Pontryagin's principle), [8] or by solving the Hamilton–Jacobi–Bellman equation (a sufficient condition). We begin with a simple example. Consider a car traveling in a straight line on a hilly ...
Theorem — Let be a positive integer. If : {: =,, >} is a set-valued function with closed graph that satisfies Walras's law, then there exists an economy with households indexed by , with no producers ("pure exchange economy"), and household endowments {} such that each household satisfies all assumptions in the "Assumptions" section except the "strict convexity" assumption, and is the excess ...
Charles S. Peirce proposed an economic theory of scientific experimentation in 1876, which sought to maximize the precision of the estimates. Peirce's optimal allocation immediately improved the accuracy of gravitational experiments and was used for decades by Peirce and his colleagues.
The drawdown duration is the length of any peak to peak period, or the time between new equity highs. The max drawdown duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred.
The new definition required a change of mathematical technique from the differential calculus to convex set theory. Their definition in effect was this: an equilibrium attainable from an endowment ω consists of an allocation x and a budget line through x and ω such that there is no point along the line which either consumer (strictly) prefers ...