Anticipative information in a Brownian-Poisson market: the binary information

The binary information collects all those events that may or may not occur. With this kind of variables, a large amount of information can be captured, in particular, about financial assets and their future trends. In our paper, we assume the existence of some anticipative information of this type in a market whose risky asset dynamics evolve according to a Brownian motion and a Poisson process. Using Malliavin calculus and filtration enlargement techniques, we compute the semimartingale decomposition of the mentioned processes and, in the pure jump case, we give the exact value of the information. Many examples are shown, where the anticipative information is related to some conditions that the constituent processes or their running maximum may or may not verify