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| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Hazard Processes and Martingale Hazard Processes |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | Mathematical Finance |
| Publisher | Wiley-Blackwell Publishing, Inc. |
| Geographical Reach | international |
| ISSN | 0960-1627 |
| Volume | 22 |
| Number | 3 |
| Page Range | 519 - 537 |
| Date | 2012 |
| Abstract Text | In this paper, we build a bridge between different reduced-form approaches to pricing defaultable claims. In particular, we show how the well-known formulas by Duffie, Schroder, and Skiadas and by Elliott, Jeanblanc, and Yor are related. Moreover, in the spirit of Collin Dufresne, Hugonnier, and Goldstein, we propose a simple pricing formula under an equivalent change of measure. Two processes will play a central role: the hazard process and the martingale hazard process attached to a default time. The crucial step is to understand the difference between them, which has been an open question in the literature so far. We show that pseudo-stopping times appear as the most general class of random times for which these two processes are equal. We also show that these two processes always differ when $\tau$ is an honest time, providing an explicit expression for the difference. Eventually we provide a solution to another open problem: we show that if $\tau$ is an arbitrary random (default) time such that its Azéma's supermartingale is continuous, then $\tau$ avoids stopping times. |
| Digital Object Identifier | 10.1111/j.1467-9965.2010.00471.x |
| Other Identification Number | merlin-id:14832 |
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