I am studying American options and inquisitive on why they lack an analytic pricing formula. I found a paper by Kim,1990 on analytic valuation of these options and then Byun,2005 paper which studies Kim,1990 analytic valuation properties.
I am afraid I have not found anything apart from that ever since 2005. Could this be the last document about the analytic pricing of American options.
(Perhaps I am mistaken or didn't do a thorough search). Could anyone suggest me some links to recent work on this area of Pricing American options using analytic formulae?
I appreciate in advance