3contingentclaimsmarkets-wenkub
2023-02-07 01:10:13 本頁面
【正文】 t of probabilities. ()()()( ) ( ) ( ) ( ) ( ) ,()( ) ( ) ( ) ( )()ssfpc sspc spc s m s s pc s E mmss s R m s sEm??? ? ????? ? ?? ? ???Then we can rewrite the asset pricing formula as: ? We use the notation E* to remind us that the expectation uses the risk neutral probabilities π *instead of the real probabilities π . ?*(s) = (m(s) / E(m)) ?(s) ? ?*gives greater weight to states with higher than average marginal utility m ? risk aversion is equivalent to paying more attention to unpleasant states, relative to their actual probability of occurrence. ? Application to report one’s reasonable subjective probabilities. ? We can also think of the discount factor m as the derivative or change of measure from the real probabilities π to the subjective probabilities ?* 連續(xù)時間 ? 在完全市場中，兩者的風險源相同。 ? From (),we have ( ) ( )fpttdp D d dpE dt r dt E dtp p p??????? ? ? ? ??— — 超 額 收 益可 見 是 風 險 價 格 。 ? Coupled with p = E(mx), we obtain the consumptionbased model again. ( ( ) )( ) ( )()( ) ( ( ) )()( ) ( )u c spc s sucpc s u c smss u c???????????marginal rates of substitution ? The investor’s first order conditions say that marginal rates of substitution between states tomorrow equals the relevant price ratio, 邊際替代率 相對價格比（經(jīng)概率調(diào)整） 1122( ) ( ( ) )( ) ( ( ) )m s u c sm s u c s???Economics behind this approach to asset pricing (figure ) Risk Sharing ? In plete markets, the prices are the same for all investors. 如果信息是透明的，每個人都知道客觀概率，則 marginal utility growth should be the same for all investors ? If investors have the same homothetic utility function (for example, power utility), then consumption itself should move in lockstep. 11( ) ( )( ) ( )ijijttijttu c u c
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