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Maybe this is not the kind of question for this website, but nevertheless I believe it could be interesting for a large audience.

I am interested to know if there is some book where the subject of actuarial mathematics is treated in a rigorous "mathematical" way, somehow suitable for graduate math students or experienced mathematicians who are interested in this subject for research reasons.

Since I am new in this field, I am interested in a kind of reference where the subject is treated from the basics to advanced topics (of course with a backgroud in probability theory or stochastic process given for granted).

Thank you

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Here are some references, where it is made precise that the rigorous mathematical framework leading to the theory is explained. 1)Term-Structure Models , a graduate course , by Damitir Filipovic (Springer 2009). 2)Risk Analysis in Finance and Insurance (2nd edition), by Alexander Melkinov (Chapman & Hall/CRC, 2011). 3)Market-Consistent Actuarial Valuation, by M.V. Wüthrich, H. Bülmann & H. Furrer (Springer 2008). 4) (in French !) : Mathématique et Assurance (first elements) by D. Pierre-Loti-Viaud & P. Boulongne (Ellipses 2014).

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