Title:  American options under asymmetric information in the predictable setting

Abstract: We study the valuation of American contingent claims with irregular payoff processes in a financial market where the buyer possesses additional information. The seller operates with respect to the public filtration, while the buyer acts under an initially enlarged filtration. In this setting, we investigate the value of the American contingent claim when the buyer exercises the option according to predictable stopping strategies, i.e. exercise rules that can be announced in advance. This formulation is particularly relevant in the absence of regularity, since enlargement may transform jump times that are totally inaccessible under the public filtration into predictable times under the enlarged one. Within this framework, the value of the American contingent claim is characterized through the solution of a reflected backward stochastic differential equation (RBSDE) in the predictable setting, and the difference between the two information structures provides a representation of the cost of the additional information.