We propose a class of financial models in which the prices of assets are L\'evy-Ito processes driven by  Brownian motion and a dynamic Poisson random measure. Each such model consists of a pricing kernel, a money market account, and one or more risky assets. The Poisson random measure is associated with an n-dimensional L\'evy process. We show that the excess rate of return of a risky asset in a pure-jump model is given by an integral of the product of a term representing the riskiness of the asset and a term representing the level of market risk aversion. The integral is over the state space of the Poisson random measure and is taken with respect to the L\'evy measure associated with the n-dimensional L\'evy process. The resulting framework is applied to a variety of different asset classes, allowing one to construct new models as well as non-trivial generalizations of familiar models.
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.
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propose a
present an overview of the broad
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an n-dimensional
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a dynamic
an independent
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Each such
The Poisson random measure is associated with an n-dimensional L\'evy process. Each
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The Poisson random measure is associated with an n-dimensional L\'evy process. We show that
We show how
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of a risky asset in a pure-jump model is given by an integral of the product of a term representing the riskiness of the asset and a term representing the level of market risk aversion. The integral is over the state space of the Poisson random measure and is taken with respect to the L\'evy measure associated with the n-dimensional L\'evy process. The resulting
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
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different
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non-trivial
interesting