Utility maximization problem and related backward stochastic PDEs

Author: Mikheil Mania
Co-authors: Revaz Tevzadze
Annotation:

We study utility maximization problem for general utility functions in an incomplete financial market model, where the dynamics of asset prices are described by an $R^d$-valued continuous semimartingale. Under some regularity assumptions on the utility function we prove that the value function is a regular family of semimartingales satisfying a backward stochastic partial differential equation. We show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As examples the cases of power, exponential and logarithmic utilities are considered.

Lecture files:

საშუალო სარგებლიანობის ოპტიმიზაციის ამოცანა და დაკავშირებული შექცეული [ka]
Utility maximization problem and related backward stochastic PDEs [en]