Structure Preserving Equivalent Martingale Measures for $\mathscr{H}$-SII Models

TL;DR

This paper establishes a relationship between structure-preserving equivalent martingale measures for semimartingale-driven financial models and a set of measurable functions, providing conditions for their existence and examples with Lévy models.

Contribution

It introduces a novel connection between martingale measures and measurable functions, extending the understanding of model conditions in semimartingale financial models.

Findings

Existence of martingale measures is equivalent to non-emptiness of a measurable function set.

Provides mild conditions for the existence of such measures in Lévy models.

Connects model characteristics with measure existence through semimartingale properties.

Abstract

In this article we relate the set of structure preserving equivalent martingale measures $(\mathcal{M})$ for financial models driven by semimartingales with conditionally independent increments to a set of measurable and integrable functions $(\mathscr{Y})$. More precisely, we prove that $(\mathcal{M}\not = \emptyset)$ if, and only if, $(\mathscr{Y}\not = \emptyset)$, and connect the sets $(\mathcal{M})$ and $(\mathscr{Y})$ to the semimartingale characteristics of the driving process. As examples we consider integrated L\'evy models with independent stochastic factors and time-changed L\'evy models and derive mild conditions for $(\mathcal{M} \not = \emptyset)$.