# Advances in Mathematical Economics by Guillaume Carlier (auth.), Shigeo Kusuoka, Toru Maruyama

By Guillaume Carlier (auth.), Shigeo Kusuoka, Toru Maruyama (eds.)

**Research Articles**: G. Carlier, Duality and life for a category of mass transportation difficulties and financial purposes; Charles Castaing and Ahmed Gamal Ibrahim: practical evolution equations ruled via m-accretive operators; Leonid Hurwcz and Marcel okay. Richter, Implicit capabilities and diffeomorphisms with no C; Leonid Hurwicz and Marcel okay. Richter, Optimization and Lagrange multipliers: Non-C1 Constraints and minimum constraint skills; Takao Fujimoto, Jose A. Silva and Antonio Villar, Nonlinear generalizations of theorems on inverse-positive matrices; Shigeo Kusuoka, Monte Carlo procedure for pricing of Bermuda style derivatives.- **Historical Perspectives**: Isao Mutoh, Mathematical economics in Vienna among the wars.- topic index.

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**Example text**

1) 2 = 2(uAn(t) - uAm(t),UAJt) - uAm(t) ) = 2(A nAAJt)UAJt) - AmAAm(t)UAm(t),UAn(t) - uAm(t)) + 2(J An(t)UAn(t) - h m(t)UAm(t),UAn(t) - uAm(t)). Here JA(t) stands for JAA(t). 5) 2 ::; 2(A nAAn(t)UAn(t) - AmAA m(t)U Am(t) , uAJt) - UAm(t) ) = -2 (A nUAn(t) - AmU Am(t) ,UAn(t) - UAm(t) ). ) - u Am( ') ) (L~{([O ,tJ) ,L~([O ,t])) ::; o. 7) and [11], (u,XJ)) converges in the Hilbert space LJI([O ,I]) . Let v be the limit of (u,XJ)) and let, for all t E [0, 1] u(t) = a + l t v(s ) ds. ) in CH([O , 1]) becau se the mapping f t-4 Jo f( s) ds from LJI([O, 1]) to Cu([O, 1]) is continuous for the norm topologies.

Step 2. Now let us go into the case when F satisfies (H 4 ) . Let us summarize the results obtained in the first step. e t E [0,1], and u(s) = cp(s), Vs E [-r, 0]. 9). Let K a denotes K equipped with the a(E , E') topology. e, (3) for every e > 0, there is a compact subset Je C [0,1] such that the Lebesgue measure of [0, 1] \ Je is less that e, and the graph of the restriction FolJe x CE([-r, 0]) is closed in Je X CE([-r, 0]) X K a , and {0} =I Fo(t, u) C F(t , u), V(t, u) E Je X CE([- r, 0]) .

Anal. Appl. 95, 344-374 (1983) ä Adv. Math . Econ. 5, 55-63 (2003) Advancesin MATHEMATICAL ECONOMICS ©Springer-Verlag 2003 Nonlinear generalizations of theorems on inverse-positive matrices* Takao Fujimoto", Jose A. jp) Department of Economic Analysis, University of Alicante, 03071 Alicante, Spain Department ofEconomic Analysis , University of Alicante and IVIE, 03071 Alicante, Spain Received: August 2, 2002 Revised: September 2, 2002 JEL classification: C67 Mathematics Subject Classification (2000): 15A48 Abstract.