  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.
