Before revision:  We propose the G-conditional full support condition by using uncertain capacity, and the  price path satisfying the G-conditional full support condition could be approximated by its G-consistent asset price system, and we derived that the bid and ask prices of the European contingent claim against such risky asset  can be expressed by discounted of some conditional G-expectation of the claim.
After revision:  We propose the G-conditional full support condition by using uncertain capacity, and the price path satisfying the G-conditional full support condition could be approximated by its G-consistent asset price systems. We derive that the bid and ask prices of the European contingent claim against such risky asset can be expressed by discounted of some conditional G-expectation of the claim.