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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 77-99 |
| Journal | Stochastics and Stochastics Reports |
| Volume | 76 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2004 |
| Externally published | Yes |