Abstract:

 The financial market with Knightian uncertainty is studied. Using the solution of BSDE and the method of time-risk discount, the dynamic pricing model of the reload stock option with two barriers is proposed. Also, the explicit solution of the model is derived. And obtaining the dynamic pricing interval of the reload stock option with two barriers is in accordance with Epstein′s conclusion. Finally, a numerical analysis is applied to depict the important impacts of the investors′ subjective sentimens to Knightian uncertainty and the up and down barrier prices on the pricing of the reload stock option with two barriers.

Key words: Knightian uncertainty; option pricing; backward stochastic differential equation; time-risk discount; reload stock option