Existence of equivalent local martingale deflators in semimartingale market models

TL;DR

This paper systematically investigates the conditions under which equivalent local martingale deflators exist in semimartingale market models, characterizing their existence via modified semimartingale characteristics and providing economic interpretations.

Contribution

It introduces a characterization of the existence of deflators using modified semimartingale characteristics, advancing understanding in financial market modeling.

Findings

Existence of deflators characterized by modified semimartingale characteristics

Examples illustrating the theoretical results

Economic interpretations of the deflators

Abstract

This paper offers a systematic investigation on the existence of equivalent local martingale deflators, which are multiplicative special semimartingales, in financial markets given by positive semimartingales. In particular, it shows that the existence of such deflators can be characterized by means of the modified semimartingale characteristics. Several examples illustrate our results. Furthermore, we provide interpretations of the deflators from an economic point of view.