We study unilateral valuation problems for American options within the framework of a general nonlinear market by extending results from Bielecki et al. [9, 12] who examined contracts of European style. A BSDE approach is used to establish more explicit pricing, hedging and exercising results when solutions to reflected BSDEs have additional desirable properties. We employ for this purpose results on solutions to BSDEs and reflected BSDEs driven by RCLL martingales obtained by Nie and Rutkowski [62, 63].
The research of T. Nie was supported by the National Natural Science Foundation of China (Nos. 12022108, 11971267, 11831010, 61961160732), Natural Science Foundation of Shandong Provincial (No. ZR2019ZD42), China Postdoctoral Science Foundation (Nos. 2018M640620 and 2019T120580) and Qilu Young Scholars Program and Distinguished Young Scholars Program of Shandong University. The research of M. Rutkowski was supported by the Australian Research Council Discovery Project DP200101550.
"American options in nonlinear markets." Electron. J. Probab. 26 1 - 41, 2021. https://doi.org/10.1214/21-EJP658