Two-time-scale Jump-Diffusion Models with Markovian Switching Regimes

Abstract

This work is concerned with two-time-scale jump diffusion models modulated by continuous-time Markov chains. One of our motivations stems from generalization of insurance risk models. The models are hybrid in the sense that they involve both continuous dynamics and discrete events. Two cases are considered. One of them has a fast-varying switching process, and the other contains a rapidly fluctuating diffusion. Two-time scale is used for complexity reduction. Using weak convergence methods, we derive their limit processes. The insight and implication provided by the analysis are: to reduce the complexity, one can ignore the detailed variations and concentrate on the limit or the reduced models.

Keywords:

• Markov chain
• Switching diffusion
• Hybrid models
• Poisson process
• Weak convergence
• 60F05
• 60J27
• 60J60
• 60J75
• 90A46

Acknowledgements

The research was supported in part by the National Science Foundation under grants DMS-0304928, and in part by Wayne State University Research Enhancement Program and by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7139/01H).

Notes

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