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In this paper,a derivative pricing model in ambiguity market was established via indifferent pricing principle and the backward stochastic differential equation description for the worst case utility in ambiguity market in Chen and Epstein [Econometrica,70(2002),1403-1443].Under some proper assumptions,it was proved that the buying price and the selling price in this model are same as the price in the standard Black -Scholes model if no investment restriction exists in the market.But if short selling is prohibited in the market,then the selling price or the buying price is different from the price in the B-S model,and it is governed by a forward-backward stochastic differential equation.In Markovian frame,we transformed the FBSDE into a PDE problem,and compare the prices of European derivatives or American derivatives in this model with the price in B-S model by PDE method.Moreover,we use the previous method to establish a convertible bond pricing model in ambiguity market,which can be described as a non-zero-sum Dynkin game problem,and transformed into a variational inequality system.Some properties of the price and the optimal calling or converting strategies are discovered by PDE method.