Let P be the true probability measure, where P() denotes the actual probability that the state

Let P be the true probability measure, where P(ω) denotes the actual probability that the state ω occurs. Define the state price density by the random variable L(ω) = Q(ω)/P(ω), where Q is a risk neutral measure. Use R_m to denote the return of the risky security m, where R_m = [S_m(1) − S_m(0)]/S_m(0), m = 1, ··· ,M. Show that E_Q[R_m] = r,m = 1, ··· ,M, where r is the interest over one period. Let E_P [R_m] denote the expectation of R_m under the actual probability measure P, show that

where cov denotes the covariance operator.

Transcribed Image Text:

Ep[Rm] r = -cov (Rm, L),