By Vol 7

Loads of fiscal difficulties could be formulated as limited optimizations and equilibration in their suggestions. a variety of mathematical theories were offering economists with integral machineries for those difficulties coming up in financial idea. Conversely, mathematicians were inspired by way of numerous mathematical problems raised by means of fiscal theories. The sequence is designed to assemble these mathematicians who're heavily drawn to getting new tough stimuli from fiscal theories with these economists who're seeking effective mathematical instruments for his or her learn. The editorial board of this sequence includes the next trendy economists and mathematicians: **Managing Editors : S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors : R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont (CREST-CNRS), N. Hirano (Yokohama nationwide Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Ohio country Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), ok. Kamiya (Univ. Tokyo), ok. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), H. Matano (Univ. Tokyo), ok. Nishimura (Kyoto Univ.), M.K. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), A. Yamaguti (Kyoto Univ./Ryukoku Univ.), M. Yano (Keio Univ.).
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**Extra resources for Advances in Mathematical Economics**

**Example text**

Moreover, for each of two problems, a duality theorem holds true, that is optimal values of the corresponding original and dual infinite linear programs are equal. These equivalence and duality remain true when X is a (not necessarily metrizable) compact space and (p is a, continuous (or merely a lower semi-continuous) function on X x X that satisfies the triangle inequality and vanishes on the diagonal [25]. ) Generalizations of the duality theorems to MKPs on non-compact (or non-topological) spaces see [14], [17], [18], [19], [23].

The method is based on duality results relating to the Monge - Kantorovich mass transportation problem (MKP), a relaxation of an old 'excavation and embankments' problem due to Caspar Monge [26]. As is shown in [20], [22], a demand function is rationalized by a given concave utility function if and only if the corresponding indirect utility function belongs to the constraint set of an infinite linear program, which is dual to the MKP with a fixed marginal diflFerence and a special cost function.

From the (ti) axiom just proved the thesis follows immediately. It remains to show that p satisfies convexity and lower semi-continuity. x {x) Z^^ [x) dx = sup [EQ [-X]; 0 < P : ^^ ~ ^ Q } . (23) Law invariant convexriskmeasures 43 Convexity: from identity (23) it follows that for any X,Y e L°° and for any a € [0,1] piaX+{l-a)Y) = snp\ Sup