Abstract
Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.
| Original language | English |
|---|---|
| Pages (from-to) | 1019-1030 |
| Number of pages | 12 |
| Journal | Journal of Applied Probability |
| Volume | 36 |
| Issue number | 4 |
| Publication status | Published - Dec 1999 |
| Externally published | Yes |
Keywords
- First passage times
- Girsanov transformation
- Numerical integration
- Werner process