Exercise 5 7 For random variable X, suppose that the moment generating function m(t) E etX exists for any t 0 Let (t) logm(t), called the cumulant generating function Prove the following (1) (t) is decreasing in t if and only if E XetX E etX (E XeX ) ...

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Exercise 5.7 For random variable X, suppose that the moment generating function m(t) = E[etX] exists for

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Exercise 5.7 For random variable X, suppose that the moment generating function m(t) = E[e−tX] exists for any t > 0. Let ϕ(t) = logm(t), called the cumulant generating function. Prove the following.

(1) ϕ(t) is decreasing in t if and only if

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Stochastic Processes With Applications To Finance

ISBN: 9781439884829

2nd Edition

Authors: Masaaki Kijima

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Exercise 5.7 For random variable X, suppose that the moment generating function m(t) = E[etX] exists for

Question:

E[XetX]E[etX] (E[XeX]).

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Stochastic Processes With Applications To Finance

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