We address the pricing of American straddle options. We use partial Laplace transform techniques due to Evans et al. (1950) to derive a pair of integral equations giving the locations of the optimal exercise boundaries for an American straddle option with a constant dividend yield.
G. Alobaidi. R. Mallier. "Laplace transforms and the American straddle." J. Appl. Math. 2 (3) 121 - 129, 18 June 2002. https://doi.org/10.1155/S1110757X02110011