arXiv:1501.03638 [math.PR]AbstractReferencesReviewsResources
Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion
Peng Jin, Barbara Rüdiger, Chiraz Trabelsi
Published 2015-01-15Version 1
In this paper we find the transition densities of the basic affine jump-diffusion (BAJD), which is introduced by Duffie and G\^{a}rleanu [D. Duffie and N. G\^{a}rleanu, Risk and valuation of collateralized debt obligations, Financial Analysts Journal 57(1) (2001), pp. 41--59] as an extension of the CIR model with jumps. We prove the positive Harris recurrence and exponential ergodicity of the BAJD. Furthermore we prove that the unique invariant probability measure $\pi$ of the BAJD is absolutely continuous with respect to the Lebesgue measure and we also derive a closed form formula for the density function of $\pi$.
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Categories: math.PR
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