Stochastic Analysis Common Seminar Series
Tuesday, October 23, 2018
4:00 PM – 5:00 PM
Stratton Hall 308
Speaker: Mauricio Enrique (Elizalde Autonomous University of Madrid)
Title: On Anticipative Portfolio Optimization
Abstract: When an investor has privileged information about the future (insider trader) of a stock or equivalently, of the driving Brownian motion, the expected-utility-theory model of his wealth changes, and the portfolio process can not be calculated in a classical way because is not adapted to the natural filtration, so one has to enlarge it or use anticipative integration. The Ito integral makes only sense when the integrand is a non-anticipating process, i.e. when the process cannot see into the future, so it could not be applied in this case if the filtration is not enlarged. There exist stochastic integrals to handle anticipative (not adapted) processes like forward and Skorohod integrals.
One of the earliest authors to approach this problem were Pikovsky and Karatzas using enlargement of filtrations. We replicated their result using three techniques:
Using a Brownian Bridge avoiding the anticipative value
Using a variational method with forward integration
Using Hida-Malliavin derivative and enlargement of filtration.