Approximate hedging strategy in the (B,S,F)-market model

The market model consisting of a stock, a risk-free asset and a cash flow ((B,S,F)-market) is considered. It is assumed that the payment is provided for short-sales. The set of the possible prices of the stock has structure of a binary tree. It is supposed that a payment function is defined on the set of terminal nodes of a tree. The work purpose is construction of a self-financed strategy providing the given value of the payment function in terminal nodes and formation of the initial portfolio of the minimum cost. The approximate algorithms with an estimated accuracy of solution of the problem are developed. Results of numerical experiments and examples are given.