References for Stochastic Calculus of Jump Processes

Summary

The document asks for a detailed introduction to stochastic calculus for Poisson and other jump processes, including random intensities and jump sizes. It notes that standard derivative-pricing texts tend to emphasize Brownian motion, with jump-diffusion models receiving limited treatment.

The responses recommend a progression through introductory and more specialized material: a chapter by Nicolas Privault for a brief overview, Shreve’s treatment of jump processes as a starting point, Cont and Tankov for broader coverage, and selected chapters by Jeanblanc and coauthors. The evidence is a set of reader recommendations rather than a comparison or evaluation of the texts. The discussion does not explain the calculus itself, assess each book’s prerequisites or strengths in detail, or provide coverage of stochastic control beyond noting it as a possible interest.

Key ideas

• The question concerns stochastic calculus for Poisson processes with random intensity and jump sizes.
• Brownian motion dominates many standard finance texts, while jump processes may receive only brief treatment.
• Shreve’s introduction is suggested as a starting point before more specialized jump-process texts.
• The recommendations are pointers to further study, not a technical explanation or systematic review.

Tags

# How do I learn the stochastic calculus of Poisson processes?


# How do I learn the stochastic calculus of Poisson processes?












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)

## Answer by nbbo2 (score 3, accepted)

https://quant.stackexchange.com/a/33140

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.