Anticipative information in a Brownian-Poissonmarket: the binary information

TL;DR

This paper investigates how anticipative binary information affects asset dynamics in a market driven by Brownian motion and Poisson processes, using advanced calculus techniques to quantify the information's impact.

Contribution

It introduces a method to compute the semimartingale decomposition of asset processes with anticipative binary information in a combined Brownian-Poisson market.

Findings

Exact value of anticipative information in pure jump case

Semimartingale decomposition formulas derived

Examples relate information to process conditions

Abstract

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.