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

ISBN-10: 4431000038

ISBN-13: 9784431000037

ISBN-10: 4431539794

ISBN-13: 9784431539797

**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 by way of m-accretive operators; Leonid Hurwcz and Marcel ok. Richter, Implicit features 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 approach for pricing of Bermuda sort derivatives.- **Historical Perspectives**: Isao Mutoh, Mathematical economics in Vienna among the wars.- topic index.

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**Additional info for Advances in Mathematical Economics**

**Example text**

8 < + 00. Since the operator A(t ö) satisfies (H2 ) , Pick 8> such that Ilall there is 0(8) such that IIJenA(tö)a - ° all:::; eno(8). Let p as in (Hd . There is "( > such that IIp(t)11 :::; ~ for an t E [0,1] . By using (Hd and the preced ing inequality, we obtain the estimate Il xk - all s IIJenA( t k) Xk_l - JenA(t k)all + IIJenA(t k)a - JenA(tö)all + IIJenA(t ö)a - all :::; Il x k- l - all + en"(L(llall) + eno(8) = Il xk-l - all + en("(L(llall) + 0(8)). , n . , n . 7) and (H 2 ) there is (( ß) > such that IIJenA(tÖ)x k - xk ll :::; en( (ß) .

8) we have the estimate Ilun(Bn(t)) - wn(t)11 :::; enlp(Bn(t )) - p(t)IL(llun(8n(t)) + engn(t)ID :::; enlp(Bn(t)) - p(t)IL(ß + IKI). 13) lim wn(t) = u(t), Vt E [0,1]. ,oo Let n ~ 1 and let t E]O, 1[. 11) and the preceding estimate into account, we get °::; k < 1. So, taking Functional evolution equations govemed by m-accretive operators 33 d(- un(t ) + gn(t) , A(t)wn (t )) = d (U n(8n(t )) - un((}n (t)) + gn(t ), A(t)Wn(t) ) en 1 S; -llun((}n(t)) - wn(t) 11 en S; IP((}n (t)) - p(t )IL(ß + IKI).

Suppose that A(t) : E --+ cc( E) U {0} ; t E [0,1], is an maccretive operator satisfy ing (H 1 ) , (H2 ) , (H3 ) and C : [0,1] --+ Eis a closed ball- compa ct valued, (that is, Vt E [0,1], C(t) is closed and its intersection with any closed ball of Eis compact) upper semicontinuous multifunction satisfying : (*) 0 E C(t),for all tE [0,1] and (**) [Je + 'xA(t)]-l C(S) c C(t) , f or all ,X > 0 andfor all 0 ::; s ::; t ::; 1. e t E [0,1], { u( O) = a , u(t ) E C(t) n D , Vt E [0,1]. Prooj. 4, so we do not want to go into details too much .

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

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