A numeraire-free and original probability based framework for financial markets

TL;DR

This paper introduces a novel, numeraire-free probability framework for financial markets, reformulating key concepts like fair markets and superhedging using martingale deflators, and reviews related portfolio optimization and utility-based pricing methods.

Contribution

It presents a new probability-based approach that is independent of numeraire choice, unifying and extending existing theories in financial market modeling.

Findings

Reformulation of fair markets and superhedging in terms of martingale deflators

Characterization of complete markets within the new framework

Review of utility-based contingent claim pricing in incomplete markets

Abstract

In this paper, we introduce a numeraire-free and original probability based framework for financial markets. We reformulate or characterize fair markets, the optional decomposition theorem, superhedging, attainable claims and complete markets in terms of martingale deflators, present a recent result of Kramkov and Schachermayer (1999, 2001) on portfolio optimization and give a review of utility-based approach to contingent claim pricing in incomplete markets.