Advances in mathematical economics, Volume 8 by S. Kusuoka, A. Yamazaki

By S. Kusuoka, A. Yamazaki

Loads of fiscal difficulties can formulated as restricted optimizations and equilibration in their solutions.Various mathematical theories were offering economists with crucial machineries for those difficulties coming up in financial concept. Conversely, mathematicians were prompted through a number of mathematical problems raised through fiscal theories. The sequence is designed to collect these mathematicians who have been heavily attracted to getting new demanding stimuli from fiscal theories with these economists who're looking for powerful mathematical instruments for his or her researchers.

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Extra resources for Advances in mathematical economics, Volume 8

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NE. But, from [ 14, Theorem 2. 1 . c. mapping h : [0, 1] x X -. 2) with h = r}[0,1] xX h(t, x) df-Lf(x) dt > - xX h(t, x) df-Lt(x) dt. f, we thus have f(t, x) df-Lt (x) dt < which proves (3. 1). r}[0,1] r}[0,1] xX < lim inf < lim inf a a i(t, x) df-Lt(x) dt r}[0,1] {}[0,1] xX xX i(t, x) dJLf(x) dt f(t, x) dJLf(x) dt + EM, D 40 C. Castaing, P. Raynaud de Fitte, A Salvadori Some epiconvergence results. We now continue with some limiting proper­ ties of a sequence of variational inequalities given by normal integrands.

Let E dom an ele­ of f at the point ment ( E E' belongs to the proximal subdifferential f)P E dom if there exist real numbers r5 > 0 such that x f(x) a, f(y) > f(x) + (, Y - x) -a l Y - x l 2 f, x ff, : ____. ( x for all y E + r5BJE ( O , 1) where BJE ( O , 1) is the closed unit ball in E. Now we want to extend the preceding notion to the proximal subdifferential of f)P 1 of the lower semicontinuous integral functionals 1 defined on the space L]ffi ( [O , 1]) equipped with the usual norm JH[ being a separable Hilbert space.

A new proof of existence of equilibrium in incomplete markets economies. J. Math. Econ. : Discreteness of equilibria in incomplete markets with a continuum of states. J. Math. Econ. : Default and exogenous collateral in incomplete markets with a contin­ uum of states. J. Math. Econ. , Siconolfi, P. : Generic existence of competitive equilibria with restricted participation. J. Math. Econ. : Existence of equilibrium plans, prices, and price expectations. : Convex Analysis. : Equilibrium in economies with financial incomplete markets.

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