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We model a nonlinear price curve quoted in a market as the utilityindifference curve of a representative liquidity supplier. As the utilityfunction we adopt a g-expectation. In contrast to the standard framework offinancial engineering, a trader is no more price taker as any trade has apermanent market impact via an effect to the supplier's inventory. The P&L of atrading strategy is written as a nonlinear stochastic integral. Under thismarket impact model, we introduce a completeness condition under which anyderivative can be perfectly replicated by a dynamic trading strategy. In thespecial case of a Markovian setting the corresponding pricing and hedging canbe done by solving a semi-linear PDE.

Perfect hedging under endogenous permanent market impacts