By Shigeo Kusuoka, Toru Maruyama
A lot of monetary difficulties might be formulated as limited optimizations and equilibration in their suggestions. a variety of mathematical theories were offering economists with quintessential machineries for those difficulties coming up in financial idea. Conversely, mathematicians were motivated by way of a number of mathematical problems raised through monetary theories. The sequence is designed to assemble these mathematicians who're heavily drawn to getting new demanding 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
With Applications in Control Theory and Probability Theory. Kluwer Academic, Dordrecht (2004) 15. : Some limit results for integrands and Hamiltonians with application to viscosity. J. Nonlinear Convex Anal. 6(3), 465–485 (2005) 16. : Some variational convergence results with application to evolution inclusions. Adv. Math. Econ. 8, 33–73 (2006) 17. : On a optimal control problem governed by the sweeping process (2013). Preprint 18. : On a Skorohod problem (2013). Preprint 19. : On the Pettis integral of closed valued multifunction.
2) Optimal Control Problems Governed by a Second Order Ordinary . . 1. Let J : [0, 1] × E × Y × Z → R be a bounded continuous integrand, τ, σ ∈ [0, 1] such that τ ∈ [0, η1 [ and τ + σ < 1 and let us consider the upper value function 1 UJ (τ, x) = sup inf α∈ (τ ) z∈Z(τ ) J (t, uτ,x,α(z),z (t), α(z)(t), z(t))dt , τ τ ∈ [0, η1 ], x ∈ E. where uτ,x,α(z),z is the trajectory WE2,1 ([τ, 1])-solution of second order differential game ⎧ u¨ τ,x,α(z),z (t) + γ u˙ τ,x,α(z),z (t) = F (t, α(z)(t), z(t)), t ∈ [τ, 1], τ ∈ [0, η1 ] ⎪ ⎪ ⎪u ⎨ (τ ) = x, τ,x,α(z),z ⎪ ⎪ ⎪ ⎩ uτ,x,α(z),z (1) = m−2 αi uτ,x,α(z),z (ηi ).
Vietnam J. Math. 24(3), 241–286 (1996) 7. : Evolution inclusions with pln functions and application to viscosity and controls. J. Nonlinear Convex Anal. 8(2), 227–255 (2007) 8. : On the fiber product of Young measures with applications to a control problem with measures. Adv. Math. Econ. 6, 1–38 (2004) 9. : Second order differential inclusions with m-points boundary condition. J. Nonlinear Convex Anal. 12(2), 199–224 (2011) 10. : Some topological properties of solutions set in a second order inclusion with m-point boundary condition.
Advances in mathematical economics. Vol.18 by Shigeo Kusuoka, Toru Maruyama