Utility maximization in the large markets

TL;DR

This paper studies utility maximization in large financial markets with countably many assets, providing theoretical results and characterizations of the value function in such models.

Contribution

It extends utility maximization theory to large markets with infinitely many assets, linking the large market problem to finite-dimensional models.

Findings

Established the existence of optimal strategies in large markets.

Characterized the value function via finite-dimensional approximations.

Reinforced the applicability of utility maximization principles in complex market models.

Abstract

In the large financial market, which is described by a model with countably many traded assets, we formulate the problem of the expected utility maximization. Assuming that the preferences of an economic agent are modeled with a stochastic utility and that the consumption occurs according to a stochastic clock, we obtain the "usual" conclusions of the utility maximization theory. We also give a characterization of the value function in the large market in terms of a sequence of the value functions in the finite-dimensional models.