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



Rigorous introductions to actuarial mathematics
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).


