RDP 2016-07: The Efficiency of Central Clearing: A Segmented Markets Approach Equation (B2)

p m,t β 𝔼 t [ u ′ ( c m,t+1 ) u ′ ( c m,t ) ( p m,t+1 +( 1− λ m ) f m,t+1 + λ m [ M( y m,t+1 ) y m,t+1 +( 1−M( y m,t+1 ) ) f m,t+1 +D( y m,t+1 )max( 0,Z−[ f m,t+1 − y m,t+1 ] )+( 1−D( y m,t+1 ) )Z ] ) ] − λ m Z− λ m 1 2 𝔼 t [ M( y m,t+1 ) y m,t+1 +( 1−M( y m,t+1 ) ) [ f m,t+1 −D( y m,t+1 )min( Z, f m,t+1 − y m,t+1 ) ] ] ∫ 0 1 λ n λ ¯ u ′ ( c n,t )+ u ′ ( c ˜ n,t ) u ′ ( c m,t ) dn MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@160A@