principles of financial economics leroy and werne phần 2 pps

...  2 . The inner product of two vectors x and y isgiven byx ·y = (x11+ x 2  2 ) ·(y11+ y 2  2 ). (17 .20 )Since 1 and  2 are orthonormal, we havex ·y = x1y1+ x 2 y 2 , (17 .21 )so ... KERNELS and  y1 2 =  xZ1− xZ 2  2 +  y 2  2 . (17.15)Eqs. 17.14 and 17.15 imply that xZ1− xZ 2  2 = 0 (17.16)so, by the strict positivity of inner products, xZ1= xZ 2 .✷If ... portfolio (h1, h 2 ). Substituting 17.39 in 17.37 and 17.38 we obtain 2 3=13h1+13(h1+ h 2 ), (17.40) and 2 3=13(h1+ h 2 ) +13h 2 . (17.41)The solution is h1= h 2 = 2/ 3 which giveske= 2 3,43, 2 3....

... implies thath 2 (ξg) ≥ 2, h 2 (ξg) ≥ 1, h 2 (ξb) ≥ 1, h 2 (ξb) ≥ 0, (24 .8)h1(ξ0) + 0.9(h 2 (ξ0) −h 2 (ξg)) ≥ 0, and h1(ξ0) + 0.8(h 2 (ξ0) −h 2 (ξb)) ≥ 0. (24 .9)The solution ... positive and nonzero payoff, and (2) utility functions are strictly increasing at any date at which that payoff is nonzero. 21 9 22 0 CHAPTER 22 . MULTIDATE ARBITRAGE AND POSITIVITY 22 .3 Arbitrage and ... x1(ξbg) = 0, (23 .1) and x 2 (ξg) = x 2 (ξb) = 0, x 2 (ξgg) = x 2 (ξbb) = 0, x 2 (ξgb) = x 2 (ξbg) = 1. (23 .2) The one-period payoff matrix in each date-1 event is of rank two. However,...