Abstract： 

This paper investigates derivatives pricing under existence of liquidity costs and market impact for the underlying asset in continuous time. Firstly, we formulate the charge for the liquidity costs and the market impact on the derivatives prices through
a stochastic control problem that aims to maximize the marktomarket value of the portfolio less the quadratic variation
multiplied by a risk aversion parameter during the hedging period and the liquidation cost at maturity. Then, we obtain the derivatives price by reduction of this charge from the premium in the Bachelier model. Secondly, we consider a second order semilinear partial differential equation (PDE) of parabolic type associated with the control problem, which is analytically solved or approximated by an asymptotic expansion around a solution to an explicitly solvable nonlinear PDE. Finally, we present
numerical examples of the pricing for a variance option and a European call option, and show comparative static analyses. 