The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions

TL;DR

This paper extends the fundamental theorem of asset pricing to models with short sale restrictions and explores the hedging problem linked to claim maximality in such markets.

Contribution

It proves the fundamental theorem under short sales prohibitions and introduces a new approach to hedging and claim maximality in these constrained models.

Findings

Fundamental theorem established with short sale constraints.

Extended Ansel and Stricker's result for nonnegative semimartingales.

Connected hedging strategies to claim maximality.

Abstract

This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a well-known result of Ansel and Stricker. In the second part we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims.