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Topic Title: doleans dade exponential
Created On Sun Mar 16, 08 11:52 PM
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Alekk
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Sun Mar 16, 08 11:52 PM
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Hi all,

I am struggling with the following exercice. Suppose that X_t is a Levy process with characteristic triplet (b, c, mu(dx)). Then it is not hard to see that there exists a Levy process Z_t such that

where is the Doleans-Dade exponential of Z_t. How would you compute the characteristic triplet of Z_t. It is quite clear that the brownian part of Z_t is the same as the brownian part of X_t. What about the drift and the Levy measure ?

many thanks,
Alekk

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Stale
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Posts: 208
Joined: Nov 2006

Tue Mar 18, 08 12:25 PM
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Hi there Alekk,

the result you are looking for can be found in Goll & Kallsen, "Optimal portfolios for logarithmic utility", Stochastic Proces. Appl. nr.89, 2000.

Alternatively, look up the result in Financial Modelling with Jump Diffusions by Cont/Tankov.

Regars,
Stale
 
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Alekk
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Posts: 97
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Wed Mar 19, 08 01:29 PM
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Thank you

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