# Equivalent martingale measures for L\'evy-driven moving averages and related processes

## TL;DR

This paper establishes sufficient and necessary conditions for the existence of equivalent martingale measures in Levy-driven moving averages and related jump processes, advancing the mathematical understanding of these non-Markovian models.

## Contribution

It provides new criteria for martingale measure existence in Levy-driven moving averages, including necessary conditions for alpha-stable processes, using advanced stochastic exponential techniques.

## Key findings

- Conditions for martingale measures are both sufficient and necessary under mild assumptions.
- Explicit criteria for alpha-stable Levy processes with alpha in (1,2].
- Enhanced understanding of non-Markovian jump process models in finance.

## Abstract

In the present paper we obtain sufficient conditions for the existence of equivalent martingale measures for L\'{e}vy-driven moving averages and other non-Markovian jump processes. The conditions that we obtain are, under mild assumptions, also necessary. For instance, this is the case for moving averages driven by an $\alpha$-stable L\'{e}vy process with $\alpha \in (1,2]$. Our proofs rely on various techniques for showing the martingale property of stochastic exponentials.