Approximate hedging with proportional transaction costs in stochastic volatility models with jumps

We extend the resutls for the problem of option replication under proportional transaction costs in \cite{Nguyen} to more general frameworks where stochastic volatility and jumps are combined to capture market's important features. In particular, we study the hedging error due to discrete readjustments by applying the Leland adjusting volatility principle to compensate transaction costs. In such contexts, jumps risk is approximately eliminated and the results established in \cite{Nguyen} are recovered.