Pricing options on stocks driven by Ornstein-Uhlenback process

The pricing European option on a stock whose price process is driven by exponential Ornstein_Uhlenback process is considered. Under the conditions of the stock with paying dividends and without paying during the effective date, the problems of European option pricing are disscused by using the approach of insurance actuary pricing and arbitrage pricing respectively. The formulas of the pricing European option are obtained for the stock whose price process is driven by exponential O_U process by the above two approaches. Then, the relation between insurance actuary pricing and no-arbitrage pricing is discussed . We prove that insurance actuary pricing is arbitrage under the exponentila O-U process model.