Basic affine jump diffusion

In probability theory, a basic affine jump diffusion (basic AJD) is a Z of the form

where ${\displaystyle B}$ is a standard Brownian motion, and ${\displaystyle J}$ is an independent compound Poisson process with constant jump intensity ${\displaystyle l}$ and independent exponentially distributed jumps with mean ${\displaystyle \mu }$. For the process to be well defined, it is necessary that ${\displaystyle \kappa \theta \geq 0}$ and ${\displaystyle \mu \geq 0}$. A basic AJD is a special case of an affine process and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross (CIR) process is a special case of a basic AJD.

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