The paper is devoted to optimal superreplication of European options in the discrete setting under proportional transaction costs on the underlying asset. In particular, general pricing and hedging algorithms are developed. This extends previous work by many authors, which has been focused on...

Dynamic programming algorithms are developed for computing the ask and bid prices of American contingent claims in a binary tree setting in the presence of small proportional transaction costs, extending the recursive construction of the Snell envelope. Associated with the pricing algorithms are...