TITLE: Rigorous introductions to actuarial mathematics
QUESTION [5 upvotes]: 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

REPLY [2 votes]: 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).