hawkes processes in financial markets

In this paper, we first consider the delta computation of some options when the underlying asset is driven by a hawkes process, using a powerful tool called malliavin calculus. we will obtain an expression for the weight malliavin derivative concerning the poisson space in the desired duality formula. second, the mean-variance hedging strategy is also generalized for this type of asset according to its derivatives with respect to both wiener and poisson spaces. finally, using a clarck-ocone formula, we provide a martingale representation for the maximum of a hawkes process to price a barrier option depending on the maximum of the asset.