RDP 2016-07: The Efficiency of Central Clearing: A Segmented Markets Approach Equation (B3)

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 ) ) y m,t+1 − D ˜ ( y m,t+1 )max( 0,Z−[ y m,t+1 − f m,t+1 ] )+( 1− D ˜ ( y m,t+1 ) )Z ] ) ] + λ m Z− λ m 1 2 𝔼 t [ M( y m,t+1 )[ f m,t+1 + D ˜ ( y m,t+1 )min( Z, y m,t+1 − f m,t+1 ) ] +( 1−M( y 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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@1662@