Maximizing expected utility in the Arbitrage Pricing Model

TL;DR

This paper addresses an infinite-dimensional optimization problem in the Arbitrage Pricing Model, demonstrating the existence of optimal investment strategies that maximize expected utility using advanced mathematical techniques.

Contribution

It introduces a novel approach combining probabilistic and functional analytic methods to establish the existence of optimal strategies in a complex economic model.

Findings

Existence of optimal strategies proven

Application of probabilistic techniques in economic optimization

Use of functional analysis to handle infinite dimensions

Abstract

We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal strategies for investors who maximize their expected utility.