There is no absolute consensus on whether this piece was executed by Swedish portraitist Alexander Roslin or if it is a self portrait by French painter Anne Vallayer-Coster, but there is no dispute that Madame Vallayer-Coster is the subject of the piece. (http://womenintheactofpainting.blogspot.nl/2012/10/the-artist-anne.html)
This very interesting and beautiful portrait of Anne Vallayer-Coster is more than an official portrait, it's a token of friendship and probably a present for a painting by her that he had in his possession....
For a long time it was also misinterpreted as a self-portrait.
[https://www.bukowskis.com/en/auctions/577/214-alexander-roslin-anne-vallayer-coster-1744-1818]
"Apparently a portrait of herself at the height of her success, 2 years after marriage and a member of Antoinette’s circle of women is pleasing. She looks relaxed, comfortably sexual." (https://reveriesunderthesignofausten.wordpress.com/2015/08/06/anne-vallayer-coster-1744-1818/)