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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

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An exact and explicit solution for the valuation of American put options SP Zhu 2006, Quantitative Finance 6 (3), 229-242

It's an infinite sum of double integrals with recursively defined integrands...

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