Pricing method and arbitrage-free price interval for contingent claims

Under the framework of multiple periods, this paper applies perfect hedging principle, linear programming duality principle and martingale measure theory to determining the seller's arbitrage price and buyer's arbitrage price of contingent claims. Two cases are considered. One is allowing short selling securities and allowing borrowing and lending cash, and the other is not allowing short selling securities but allowing borrowing and lending cash. The arbitrage price and the arbitrage_free price interval of the contingent claim can be obtained by solving some linear programming problems in recursive form.