Communications in Mathematical Sciences

Volume 13 (2015)

Number 3

Special Issue in Honor of George Papanicolaou’s 70th Birthday

Guest Editors: Liliana Borcea, Jean-Pierre Fouque, Shi Jin, Lenya Ryzhik, and Jack Xin

Martingales and upper bounds for American-style options

Pages: 695 – 705



Yang Wang (Brevan Howard, Citibank Plaza, Hong Kong)

Russel Caflisch (Department of Mathematics, University of California at Los Angeles)


This article presents an analytical representation of the ‘optimal’ Martingale that appears in the dual pricing formula for an American-style option, in a generic continuous setting. This representation has a hedging interpretation and could provide an approach for computing an upper bound on the price of an American-style option.


American option, Martingale, upper bound estimation, dual pricing formula

2010 Mathematics Subject Classification


Published 3 March 2015