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I'm looking for references on the stochastic calculus of Poisson processes. My books tend to focus on derivative pricing, where Brownian motion reigns supreme. Maybe some jump-diffusion models thrown in in chapter 10, but that's not what I'm looking for.

I'd like to read a book that covers the Ito calculus of Poisson processes with random intensity and jump sizes, in a detailed way like all the derivatives books present Ito calculus. (Stochastic control would be a plus, but isn't necessary)

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    $\begingroup$ I found the book by Cont and Tankov "Financial Modelling with Jump Processes" very useful. $\endgroup$ – LocalVolatility Mar 20 '17 at 15:48
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    $\begingroup$ A Chapter by Nicolas Privault gives a brief introduction to the Stochastic Calculus of Jump Processes ntu.edu.sg/home/nprivault/MA5182/… $\endgroup$ – noob2 Mar 20 '17 at 16:21
  • $\begingroup$ The last chapter of Shreve's second volume is a good start. $\endgroup$ – Gordon Mar 20 '17 at 16:39
  • $\begingroup$ As mentioned by Gordon, chapter 11 of Shreve's II volume (Stochastic Calculus for Finance II: Continuous Time Models), called "Introduction to Jump Processes" is a good starting point. Then, as mentioned by LocalVolatility, Cont and Tankov's book is an option if you want to dig further into the subject. $\endgroup$ – Daneel Olivaw Mar 20 '17 at 17:29
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    $\begingroup$ @noob2: I've read Privault's notes and I think they're great. It doesn't go into enough depth, however $\endgroup$ – user357269 Mar 20 '17 at 17:43
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Summarizing the suggestions in comments:

Nicolas Privault's chapter Stochastic Calculus of Jump Processes [available online] provides only a very brief overview.

Chapter 11 of Shreve's II volume (Stochastic Calculus for Finance II: Continuous Time Models), called "Introduction to Jump Processes" is a good starting point. Then Cont and Tankov "Financial Modelling with Jump Processes" provides more material, with an entire volume on the subject.

Another suggestion was chapters 8-11 of the book "mathematical methods for financial markets" by Jeanblanc et al.

Contributors were @LocalVolatility, @Gordon, @user357269, @DaneelOlivaw

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