By Shigeo Kusuoka, Toru Maruyama

The sequence is designed to assemble these mathematicians who're heavily attracted to getting new difficult stimuli from monetary theories with these economists who're looking potent mathematical instruments for his or her learn. loads of monetary difficulties might be formulated as limited optimizations and equilibration in their suggestions. a number of mathematical theories were offering economists with necessary machineries for those difficulties bobbing up in fiscal conception. Conversely, mathematicians were encouraged via a number of mathematical problems raised via monetary theories.

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**Additional info for Advances in Mathematical Economics Volume 20**

**Sample text**

Solé JL, Utzet F, Vives J (2007) Canonical Lévy process and Malliavin calculus. Stoch Process Appl 117:165–187 15. Wang W, Qian L, Wang W (2013) Hedging strategy for unit-linked life insurance contracts in stochastic volatility models. WSEAS Trans Math 12(4):363–373 Adv. Math. Econ. 20, 23–75 (2016) On a Fractional Differential Inclusion in Banach Space Under Weak Compactness Condition C. Castaing, C. X. Z. t/dt JEL Classification: C61, C73 Mathematics Subject Classification (2010): 34A60, 34B15, 47H10 C.

Indeed, let ; t 2 Œ0; 1, we have the estimate Z uf . t/ Ä Z 0 ˇ ˇ. t jG. s/jds: bjp , for all a; b 0 and p 20; 1, we jjuf . ˛/ 0 On a Fractional Differential Inclusion in Banach Space Under Weak. . Œ0; 1/. s/jds for all f 2 SX1 and for all t 2 Œ0; 1, it remains to check the weak compactness property. t/ is the Aumann integral of the convex weakly compact integrably bounded mapping s 7! g. Œ0; 1/. Œ0; 1/-solutions to (16). s/ds, t 2 Œ0; 1. L1E ; L1 E /-compact, by Eberlein-Smulian theorem, we may assume that .

T/jj Ä jj f jjP1 C E 1 ˛ 1 jj f jjP1 Ä MG jj f jjP1 ; 8t 2 Œ0; 1 E E On a Fractional Differential Inclusion in Banach Space Under Weak. . ˛/ 3 Fractional Differential Inclusion in Bochner Setting We summarize at first some needed results. Let E be a Banach space and let BE be the closed unit ball of E. 1. Let H E be a subset of a Banach space E such that for each " > 0, there is a weakly compact subset K such that H K C "BE . Then H is relatively weakly compact in E. Proof. See Grothendiek ([29], page 296).