Choosing Rigorous Mathematics Texts for Quantitative Finance

Summary

The document discusses how to build mathematical foundations for quantitative finance and statistics. The questioner seeks rigorous, proof-based study of relevant tools such as linear algebra, probability, set theory, stochastic calculus, and measure theory, rather than a finance text focused mainly on applying mathematics to problems. They also want clear prerequisites, exercises, and solutions, and ask for books that meet those criteria.

The replies offer broad direction rather than a detailed bibliography: one recommends studying the underlying mathematical subjects directly, while another suggests Steven Shreve’s books and an older online text as a sample. The exchange does not compare specific titles against the requested criteria, identify which topics each covers, or confirm the availability of exercise solutions. It is therefore a starting point for selecting study materials, not a complete curriculum or assessment of particular books. Readers would need to check prerequisites, proof depth, and solutions independently.

Key ideas

• The question distinguishes mathematical foundations from books focused on applying math to finance problems.
• Desired foundations include probability, linear algebra, measure theory, and stochastic calculus.
• The requested study materials should be rigorous, state prerequisites, and include exercises with solutions.
• Replies recommend studying core mathematics directly and point to Shreve’s work, without a detailed book comparison.

Tags

# Book recommendation: math toolkit for quantitative finance and statistics


# Book recommendation: math toolkit for quantitative finance and statistics












I am looking for a book which teaches mathematical topics which are relevant to master quantitative finance and statistics.

Please note, I do not mean a book which would explain how math is applied to solve problems in quantitative finance and statistics but rather a book which would teach mathematical toolkit (linear algebra, set theory, probability, stochastic calculus, measure theory, etc.) needed to further understand math applications in the above mentioned fields.

One example is this book, but I need more.

The book should:

- cover only those topics in math which are relevant for quant finance ans statistics;

- be self-contained or make clear what previous knowledge of math it relies upon;

- rigorous (no "just believe that it is true" or "we present an intuition instead of a proof");

- provide exercises with available solutions;

- be a series mathematical book (proofs are must).

Thanks!

## Answer by madilyn (score 6)

https://quant.stackexchange.com/a/16987

All the topics you've mentioned are wonderful and shouldn't be eschewed by reading some finance-oriented review book. I recommend these instead.







## Answer by GWD (score 5)

https://quant.stackexchange.com/a/16979

I would recommend the books from Steven Shreve. Here is a link to some one of his older online pdf's (1997 but nevertheless true) so you can check if that fits the bill. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.137.6951&rep=rep1&type=pdf

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