Based on the water-saving technical principle and ABA theory, a new irrigation with high potentialities method of saving water named spatio-temporal deficit controlled irrigation is proposed, which uses full irrigation, both root-zone deficit irrigation and alternate partial root-zone deficit irrigation during the whole growing period of hot pepper.

Under the assumption that the intial wealth can t replicate the given contingent claim,the paper discusses the existence of replication strategy of maximum probability,minimum defalcation and minimum defalcation which is subject to the given probability.