kleene s theorem part 2

Girsanov’s theorem and the risk-neutral measure

Girsanov’s theorem and the risk-neutral measure

...  , 2 T  T + B T    Z1 b2 = p1  T + b expf, b , 2 T g exp , 2T db 2 T ,1   Z  T + b exp , b + T 2 db =p 2T 2 T ,1  2 Z1 y exp , y2 dy (Substitute y = T + b) y = T + b = p 2 T ... we use the Girsanov Theorem to change the probability measure, means change but variances not Martingales may be destroyed or created Volatilities, quadratic variations and cross variations are ... because Z t;  t  T , is a martingale under IP 1 92 Lemma 1.54 (Baye s Rule) If X is F t-measurable and  s  t  T , then f IE X jF s = Z s IE XZ tjF s : Proof: It is clear that Z 1s ...

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