Please first read the general advice for PhD applicants to the Department of Pure Mathematics and Mathematical Statistics. Note that you are strongly encouraged to submit your application by the deadline of 3 January 2019.
Usually, entering PhD students have a background equivalent to the Cambridge Masters of Mathematics (Part III). For financial mathematics, the Part III courses Advanced Financial Models, Advanced Probability and Stochastic Calculus are essential. You may wish to look at past exam papers to see the expected level. If your background in mathematics is not at this level, you might instead choose to apply to Part III, or apply to study financial related topics in another Cambridge department.
Once your completed PhD application has been processed by the University's Graduate Admissions Office, you may be invited to arrange a meeting, either in Cambridge or by video conferencing, to further discuss your research interests, as well as your background in finance and probability theory.