  The problem of determining the European-style option price in the incomplete
market has been examined within the framework of stochastic optimization. An
analytic method based on the discrete dynamic programming equation (Bellman
equation) has been developed that gives the general formalism for determining
the option price and the optimal trading strategy (optimal control policy) that
reduces total risk inherent in writing the option.
  The basic purpose of paper is to present an effective algorithm that can be
used in practice.
  Keywords: option pricing, incomplete market, transaction costs, stochastic
optimization, Bellman equation.

Statistical Mechanics;Pricing of Securities