This paper investigates derivatives pricing under existence of liquidity costs and market impacts for the underlying asset in continuous time. Firstly, we formulate the charge for the liquidity cost and the market impact on the derivatives prices through a stochastic control problem that aims to...

This paper proposes a new hedging scheme of European derivatives under uncertain volatility environments, in which a weighted variance swap called the polynomial variance swap is added to the Black-Scholes delta hedging for managing exposure to volatility risk. In general, under these...