Advances in Mathematical Economics, Volume 3A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers. Members of the editorial board of this series consists of following prominent 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. Berkeleyer), 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 National Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Ohio State Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), K. Kamiya (Univ. Tokyo), K. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), H. Matano (Univ. Tokyo), K. Nishimura (Kyoto Univ.), M. K. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), M. Yano (Keio Univ). |
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ba)-converge Banach space BL(S Borel co{fm coherent risk measure comonotone compact space compound criteria conditionally weakly compact consider continuous function converges weakly Corollary defined definition denote dynamic programming equivalent exists a sequence expanded Markov F-measurable Fatou property Fatou's lemma fn(w fn(Xn follows Fréchet functionally closed preorder H₁ Hence II(g invariant coherent risk isotone L¹(µ law invariant coherent LE[E Let fn Levin lim inf linear lower semi-continuous mappings ƒ Markov class Math MATHEMATICAL ECONOMICS multifunction N₁ norm optimal policy past-value sets probability measures problem Proposition Radon measure recursive formula relatively weakly compact resp satisfying scalarly stochastic dominance strong stochastic dominance subdifferentials Suppose theorem 2.2 topological space topology U₁ Un(w uniformly integrable V(ẞX V+(X w-converges w-convex w-sufficient weak weakly Cauchy weakly compact Young measures αμ µ(dw