Topic
Concave function
About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.
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TL;DR: This paper characterizes two preorders over vectors, representing here income distributions, which, for the case of an order-preserving additive welfare function W, correspond to the increasing concave functions u which are more concave than u =ln x and than u ( x )=−1/ x , respectively.
3 citations
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01 Jan 1992
Abstract: A class of generalized convex functions, the hyperbolic{concave functions, is de ned, and used to characterize the collection of Hardy{ Littlewood maximal functions. These maximal functions and the probability measures associated with these maximal functions, the maximal probability measures, are used in representations and inequalities within martingale theory. A related collection of minimal probability measures is also characterized, through a class of hyperbolic{concave envelopes.
3 citations
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TL;DR: In this paper, the authors show that the market impact of volume weighted average price (VWAP) orders is convex function of a trading rate, but most empirical estimates of transaction cost are concave functions.
Abstract: The market impact (MI) of Volume Weighted Average Price (VWAP) orders is a convex function of a trading rate, but most empirical estimates of transaction cost are concave functions. How is this possible? We show that isochronic (constant trading time) MI is slightly convex, and isochoric (constant trading volume) MI is concave. We suggest a model that fits all trading regimes and guarantees no-dynamic-arbitrage.
3 citations
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TL;DR: A Barnes-Godunova-Levin type inequality for the Sugeno integral based on an (α,m)$( {\alpha,m} )$-concave function is proved and several important results are obtained.
Abstract: In this paper, a Barnes-Godunova-Levin type inequality for the Sugeno integral based on an $( {\alpha,m} )$
-concave function is proved. Some examples are given to illustrate the validity of these inequalities. Finally, several important results, as special cases of an $( {\alpha,m} )$
-concave function, are also obtained.
3 citations
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TL;DR: This work analyzes single parameter process design problems that typically entail minimizing the sum of convex and concave functions, and transforms such problems into a tractable form, and obtains sharp characterizations of the original problem.
3 citations