European option pricing with transactions costs

It is noted that pricing derivative securities in a market where risky and riskless assets can be traded is a problem which has been solved for complete markets and general functions of the underlying securities. If an investor pays transaction costs for trading in the risky securities the market is not complete and the investor´s preferences must be taken into account in the pricing of such contingent claims. In the paper, this problem is transformed into a stochastic optimal control problem, which is solved by the method of dynamic programming. Computational results are obtained for the writing price, when the writer´s risk aversion factor is wealth independent. The pricing of a European call option is determined by the proposed algorithm