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November 19th, 2019, 1:17 am
Forum: General Forum
Topic: What’s Ito’s lemma for Poisson process in this function?
Replies: 6
Views: 2409

### Re: What’s Ito’s lemma for Poisson process in this function?

Thank you. I have corrected the typo. However, in $dY_t=Z_{N_t} dN_t$, $Z_{N_t}$ is a random variable, indicating the random jump size. I think it makes sense to include an expectation w.r.t.  $Z_{N_t}$ in the drift term, as in page 26 of  http://people.ucalgary.ca/~aswish/JumpProcesses.pdf ...
November 18th, 2019, 8:53 am
Forum: General Forum
Topic: What’s Ito’s lemma for Poisson process in this function?
Replies: 6
Views: 2409

### Re: What’s Ito’s lemma for Poisson process in this function?

Thank you Alan. May I ask one more question? In page 645 of your given file, there is an Ito formula for the compensated compund Poisson process: $$f(Y_t)=f(0)+\int_0^t \!(f(Y_s)-f(Y_s-))(dN_s-\lambda ds)+\lambda \int_0^t \!(f(Y_s)-f(Y_s-))ds$$ where $dY_t=Z_{N_t} dN_t$ is a compound Poisson proc...
November 16th, 2019, 10:25 am
Forum: General Forum
Topic: What’s Ito’s lemma for Poisson process in this function?
Replies: 6
Views: 2409

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