Introductory Books on Stochastic Calculus for Finance and Beyond
Summary
The discussion recommends introductory references for learning probability, random variables, Brownian motion, Itô integration, jump processes, and stochastic calculus. Suggested books range from finance-focused texts by Steven Shreve to compact or more intuitive introductions, as well as a general treatment of stochastic integration and differential equations outside finance.
The recommendations reflect different learning needs: a structured finance application, a concise introduction, an accessible conceptual presentation, or broader mathematical foundations. The thread offers no comparison through exercises, technical detail, or independent evaluation, so readers must choose based on their background and preferred level of rigor.
Key ideas
- Stochastic calculus texts differ in how strongly they emphasize financial applications.
- Shreve’s books are recommended for learning stochastic calculus in a finance context.
- Mikosch is suggested as a compact introduction to elementary stochastic calculus.
- Wilmott’s text is described as intuitive and less academic in style.
- Protter is suggested for studying stochastic integration beyond finance.
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Full text
# Basic book on stochastic calculus, Itô and jump processes and Brownian Motion # Basic book on stochastic calculus, Itô and jump processes and Brownian Motion I was looking for a good book that explains at beginner-level the basic of stochastic calculus, probability and random variables, Itô and jump processes as well as Brownian Motion. At university we are going really fast hence I need a book to go through the basics again. Thanks a lot. ## Answer by Wane Mamadou (score 4) https://quant.stackexchange.com/a/44157 The book Stochastic calculus for finance by Steven Shreve gives a good introduction to stochastic calculus applied to finance. A whole chapter is dedicated to the Itô Integral for example. It covers a large spectrum ranging from probability theory to stochastic financial models. I strongly recommend it! ## Answer by Daneel Olivaw (score 4) https://quant.stackexchange.com/a/44159 Elementary Stochastic Calculus by Thomas Mikosch is an excellent introduction to the topic in a very compact way. Alternatively, Stochastic Calculus for Finance II: Continuous-Time Models by Steven Shreve is a more comprehensive reference which is very much oriented to applications in finance. ## Answer by ZRH (score 2) https://quant.stackexchange.com/a/44158 Consider “Paul Wilmott Introduces Quantitative Finance” if you look for an enjoyable read, good intuition and a not too academic approach ## Answer by Theodore (score 2) https://quant.stackexchange.com/a/44244 If you're interested in learning about stochastic calculus outside of the context of quant finance (which I think is a better approach than learning about it solely in the context of finance), check out Stochastic Integration and Differential Equations by Protter.
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