Laurence Carassus, Emmanuel Gobet, Emmanuel Temam
We consider a financial model with mild conditions on the dynamic of the underlying asset. The trading is only allowed at some fixed discrete times and the strategy is constrained to lie in a closed convex cone. In this context, we derive closed formulae to compute the super-replication prices of any contingent claim which depends on the values of the underlying at the discrete times above.
As an application, when the underlying follows a stochastic differential equation including stochastic volatility or Poisson jumps, we compute those super-replication prices for a range of European and American style options, including Asian, Lookback or Barrier Options.