Computing rare-event probabilities for affine models and general state space Markov processes
Abstract/Contents
- Abstract
- Rare-event simulation concerns computing small probabilities, i.e. rare-event probabilities. This dissertation investigates efficient simulation algorithms based on importance sampling for computing rare-event probabilities for different models, and establishes their efficiency via asymptotic analysis. The first part discusses asymptotic behavior of affine models. Stochastic stability of affine jump diffusions are carefully studied. In particular, positive recurrence, ergodicity, and exponential ergodicity are established for such processes under various conditions via a Foster-Lyapunov type approach. The stationary distribution is characterized in terms of its characteristic function. Furthermore, the large deviations behavior of affine point processes are explicitly computed, based on which a logarithmically efficient importance sampling algorithm is proposed for computing rare-event probabilities for affine point processes. The second part is devoted to a much more general setting, i.e. general state space Markov processes. The current state-of-the-art algorithm for computing rare-event probabilities in this context heavily relies on the solution of a certain eigenvalue problem, which is often unavailable in closed form unless certain special structure is present (e.g. affine structure for affine models). To circumvent this difficulty, assuming the existence of a regenerative structure, we propose a bootstrap-based algorithm that conducts the importance sampling on the regenerative cycle-path space instead of the original one-step transition kernel. The efficiency of this algorithm is also discussed.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2011 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Zhang, Xiaowei |
|---|---|
| Associated with | Stanford University, Department of Management Science and Engineering |
| Primary advisor | Glynn, Peter W |
| Thesis advisor | Glynn, Peter W |
| Thesis advisor | Bambos, Nicholas |
| Thesis advisor | Lai, T. L |
| Advisor | Bambos, Nicholas |
| Advisor | Lai, T. L |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Xiaowei Zhang. |
|---|---|
| Note | Submitted to the Department of Management Science and Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2011. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Xiaowei Zhang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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