By Shigeo Kusuoka, Toru Maruyama

ISBN-10: 4431554882

ISBN-13: 9784431554882

ISBN-10: 4431554890

ISBN-13: 9784431554899

The sequence is designed to collect these mathematicians who're heavily attracted to getting new tough stimuli from financial theories with these economists who're looking potent mathematical instruments for his or her study. loads of financial difficulties should be formulated as restricted optimizations and equilibration in their strategies. a variety of mathematical theories were offering economists with fundamental machineries for those difficulties bobbing up in monetary conception. Conversely, mathematicians were influenced by means of numerous mathematical problems raised through financial theories

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**Extra info for Advances in mathematical economics. Vol.19**

**Example text**

Therefore, if % is complete, transitive, and continuous binary relation and f % D f , then %D%g by the last result of Proposition 2. Second, Hosoya [6] showed the following additional result. f //. Then, %g is transitive if and only if f satisfies the strong axiom. If f D f % for some complete and transitive binary relation %, then it satisfies the strong axiom. This fact show that if f D f % for some complete and transitive (and not necessarily continuous) binary relation %, then %g is the unique complete, transitive, and continuous binary relation that satisfies f D f % .

Therefore, if % is complete, transitive, and continuous binary relation and f % D f , then %D%g by the last result of Proposition 2. Second, Hosoya [6] showed the following additional result. f //. Then, %g is transitive if and only if f satisfies the strong axiom. If f D f % for some complete and transitive binary relation %, then it satisfies the strong axiom. This fact show that if f D f % for some complete and transitive (and not necessarily continuous) binary relation %, then %g is the unique complete, transitive, and continuous binary relation that satisfies f D f % .

RnCC /. f /. f / with respect to the local C 1 topology. f ///. Then, the next question naturally arises: does there uniquely exist a 11 See Theorem 1 of Hosoya [6]. Dfk /k converges to Df uniformly on U. RnC /2 such that f % D f ? %f continuous with respect to the local C 1 topology? However, the answer to this question is negative. R2CC /2 that is represented by a C 1 -class utility function, and two different indifference curves of % have the same limit point. In this case, any extension of % into the complete binary relation of R2C is either not continuous or not transitive.

### Advances in mathematical economics. Vol.19 by Shigeo Kusuoka, Toru Maruyama

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