OPTION PRICING FOR INCOMPLETE MARKETS VIA STOCHASTIC OPTIMIZATION: TRANSACTION COSTS, ADAPTIVE CONTROL AND FORECAST

The problem of determining the European-style option price in incomplete markets is examined within the framework of stochastic optimization. An analytic method based on the stochastic optimization is developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal feedback control) that reduces the total risk inherent in writing the option. The cases involving transaction costs, the stochastic volatility with uncertainty, stochastic adaptive process, and forecasting process are considered. A software package for the option pricing for incomplete markets is developed and the results of numerical simulations are presented.