Risk-neutral pricing for APT

TL;DR

This paper develops a mathematical framework for pricing and hedging in the Arbitrage Pricing Theory model, using advanced probabilistic and functional analysis techniques to characterize super-replication costs and optimal investment strategies.

Contribution

It introduces a dual characterization of super-replication costs and proves the existence of optimal strategies and the convergence of reservation prices in the APT setting.

Findings

Dual characterization of super-replication cost

Existence of optimal investor strategies

Reservation prices converge to super-replication cost as risk-aversion increases

Abstract

We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost. Then, we show the existence of optimal strategies for investors maximizing their expected utility and the convergence of their reservation prices to the super-replication cost as their risk-aversion tends to infinity.