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 system, and we derived that the bid and ask prices of the European contingent claim against such risky asset under uncertain can be expressed by discounted of some conditional G-expectation of the claim.