Abstract: The financial market with Knight uncertainty is studied.Assuming the underly ing stock asset follows geometric Brownian motion,the models of maximal and minimal pricing of reload stock option are built.Moreover,applying the theories of backw ard stochastic differential equation and partial differential equation,the models have been converted.At last the explicit solutions of the models have been given by using the theory of stochastic processes.And this paper depicts the important impact of Knight uncer tainty on the pricing of reload stock option through numerical analysis.

Key words: Knight uncertainty, reload stock option, robust pricing, BSDE