3contingentclaimsmarkets(文件)
【正文】 u c u c?? ???????11ijttijttcccc???? It means that shocks to consumption are perfectly correlated across individuals. ? It doesn’t say that expected consumption growth should be equal。在上圖中，pc(1)pc(2),所以 pc線較陡。 the riskfree return lies on the intersection of the 450 line (same payoff in both states) and the price = 1 plane (the set of all returns). 演講完畢，謝謝觀看！ 。 The contingent claims price vector pc points in to the positive orthant. ? m(s) = βu’[c(s)]/u’(c) Now, marginal utility should always be positive (people always want more), so the marginal rate of substitution and discount factor are always nonnegative, m0 and pc 0. ? m 0 means the realization of m is positive in every state of nature, or, equivalently every element of the vector m is positive. The set of payoffs with any given price lie on a (hyper)plane perpendicular to the contingent claim price vector. ? Since the price of the payoff x must be given by its contingent claim value, p(x) =∑pc(s)x(s) ? Interpreting pc and x as vectors, this means that the price is given by the inner product of the contingent claim price and the payoff. ? If two vectors are orthogonal —— if they point out from the origin at right angles to each other —— then their inner product is zero. ? The set of all zero price payoffs must lie on a plane orthogonal to the contingent claims price vector, as shown in figure 7. The inner product of two vectors x and pc equals the product of the magnitude of the projection of x onto pc times the magnitude of pc. where means the length of the vector x ? Since all payoffs on planes (such as the price planes in figure 7) that are perpendicular to pc have the same projection onto pc, they must have the same price. ( ) ( ) ( ) ( | )sp x pc s x s pc x pc proj x pc? ? ? ? ??x? Planes o
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