Hedging American contingent claims with constrained portfolios under a higher interest rate for borrowing

The paper studies the hedging problem of American contingent claims (ACCs) in a finance market with two kinds of frictions in the form of a higher interest rate for borrowing than for lending and constraints on portfolios selection. The setting is that of a continuous-time Itô process model for the underlying assets. Under the above-mentioned frictions, the upper-hedging price hup(K) and lower-hedging price hlow(K) of ACC are obtained by introducing auxiliary frictionless financial markets, which reflect the above-mentioned frictions. Furthermore, based on the principle of absence of arbitrage, we have that [hlow(K), hup(K)] is the interval of arbitrage-free prices of ACC.