Assume that random variables

xk = ln Rkt+1 ,

yi = ln( biu

0

i

(cit+1)

u

0

i

(cit)

)

are bivariate normally distributed with expectations

(E [ln Rkt+1] ; E h

ln( biu

0

i

(cit+1)

u

0

i

(cit)

)

i

) = (k

; c

)

and the variance-covariance matrix

V =

2

k

kc

kc

2

c

;