Anticipative information in a Brownian-Poisson market Articles uri icon

authors

  • D AURIA, BERNARDO
  • SALMERON GARRIDO, JOSE ANTONIO

publication date

  • November 2022

International Standard Serial Number (ISSN)

  • 0254-5330

Electronic International Standard Serial Number (EISSN)

  • 1572-9338

abstract

  • The anticipative information refers to some information about future events that may be disclosed in advance. This information may regard, for example, financial assets and their future trends. In our paper, we assume the existence of some anticipative information 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 derive the information drift of the mentioned processes and, both in the pure jump case and in the mixed one, we compute the additional expected logarithmic utility. Many examples are shown, where the anticipative information is related to some conditions that the constituent processes or their running maximum may verify, in particular, we show new examples considering Bernoulli random variables.

subjects

  • Statistics

keywords

  • optimal portfolio; malliavin calculus; clark-ocone formula; insider information; value of the information