  In a market with transaction costs, the price of a derivative can be
expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In
this paper, we consider a market with binomial model for stock price and
discuss how to generate the price systems. From this, the price formula of a
derivative can be reformulated as a stochastic control problem. Then the
dynamic programming approach can be used to calculate the price. We also
discuss optimization of expected utility using price systems.
