Gentlemen, let's broaden our minds. The painting, entitled "The Blue Boy," hails from the 18th century, a portrait and historical costume study by Thomas Gainsborough. While it currently resides in the Huntington Library in San Marino, California, it made at least one notable stop on its way there — in Gotham City, circa 1989.
Yes, "The Blue Boy" was featured, albeit briefly, in Tim Burton's Batman. The scene in question features Nicholson's Joker leading a group of devotees through Gotham's Flugelheim Museum after gassing the building's occupants. Together, they repaint some Rembrandts and defile Degas, all with the help of Prince's "Partyman" as a backing track. Joker seems at least a little inspired by "The Blue Boy," striking a similar pose to its subject just before one of his goons trashed it with a can of spray paint. Clearly he didn't like it as much as Francis Bacon's "Figure with Meat," which he stops Bob from hacking with a bowie knife, but any response to a piece of art is worth celebrating.
While it's not clear whether the inclusion of "The Blue Boy" was a deliberate Joker Easter egg on the part of director Todd Phillips, it would be a bizarre coincidence if it wasn't. File it under unanswerable Batman questions, along with "where does he get those wonderful toys?"