# L\'evy-Ito Models in Finance

## TL;DR

This paper reviews Le9vy-Ito models in finance, explaining how they incorporate jumps in asset prices and relate risk to return, with applications across various asset classes.

## Contribution

It provides a comprehensive overview of Le9vy-Ito models, detailing their structure, how they model risk and return, and their applications to different asset classes.

## Key findings

- Calculates excess return rates in jump models
- Connects risk with asset price jumps
- Extends traditional models to include jumps

## Abstract

We present an overview of the broad class of financial models in which the prices of assets are L\'evy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is associated with an $n$-dimensional L\'evy process. Each model consists of a pricing kernel, a money market account, and one or more risky assets. We show how the excess rate of return above the interest rate can be calculated for risky assets in such models, thus showing the relationship between risk and return when asset prices have jumps. The framework is applied to a variety of asset classes, allowing one to construct new models as well as interesting generalizations of familiar models.