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