RDP 2016-07: The Efficiency of Central Clearing: A Segmented Markets Approach Equation (27)

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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@170D@