By Shigeo Kusuoka, Toru Maruyama
A lot of monetary difficulties may be formulated as restricted optimizations and equilibration in their recommendations. quite a few mathematical theories were providing economists with imperative machineries for those difficulties bobbing up in monetary conception. Conversely, mathematicians were motivated via a variety of mathematical problems raised via monetary theories. The sequence is designed to collect these mathematicians who're heavily attracted to getting new tough stimuli from monetary theories with these economists who're looking powerful mathematical instruments for his or her research.
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Additional info for Advances in mathematical economics. Vol.18
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24 C. Castaing et al. where vτ +σ,u τ,x,f 1 (τ +σ ),g 2 (t) denotes the trajectory solution on [τ + σ, 1] associated with the control g 2 ∈ SZ1 starting from uτ,x,f 1 (τ + σ ) at time τ + σ to ⎧ v¨τ +σ,u 1 (τ +σ ),g 2 (t) + γ v˙τ +σ,u 1 (τ +σ ),g 2 (t) = g 2 (t), ⎪ ⎪ τ,x,f τ,x,f ⎪ ⎪ ⎪ t ∈ [τ + σ, 1] ⎪ ⎪ ⎨ (SODE) vτ +σ,uτ,x,f 1 (τ +σ ),g 2 (τ + σ ) = uτ,x,f 1 (τ + σ ), ⎪ ⎪ m−2 ⎪ ⎪ ⎪ ⎪ (1) = αi vτ +σ,u 1 (τ +σ ),g 2 (ηi ). v ⎪ τ +σ,u 1 (τ +σ ),g 2 ⎩ τ,x,f τ,x,f i=1 Let us set f := 1[τ,τ +σ ] f 1 + 1[τ +σ,1] f 2 .
Advances in mathematical economics. Vol.18 by Shigeo Kusuoka, Toru Maruyama