Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion
Abstract
In this paper we find the transition densities of the basic affine jump-diffusion (BAJD), which is introduced by Duffie and Garleanu [D. Duffie and N. Garleanu, 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 $\pi$.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2015
- DOI:
- 10.48550/arXiv.1501.03638
- arXiv:
- arXiv:1501.03638
- Bibcode:
- 2015arXiv150103638J
- Keywords:
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- Mathematics - Probability;
- Primary: 60H10;
- Secondary: 60J60
- E-Print:
- 21 papes