Stochastic analysis applied to portfolio optimization with Target Information

Abstract

This thesis deals with the problem of optimizing portfolios with target information in different contexts. First, we study the problem for an insider trader, who has privileged information about the future. This information is described by different filtrations, which gives problems of adaptability of the solutions, and generates the need to use stochastic calculus that generalizes that of Itô. Thus, we base our analysis comparing the optimization using the Russo-Vallois forward integration and the Skorokhod integration in the stochastic calculus. On the other hand, we deal with a problem of cost-efficient consumption, where the investor models her consumption in multiple periods with a family of target distribution and a dependency structure between them that models her preferences, and we seek for the strategy with the lowest cost which is adapted to such preferences