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# Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk

## Author

Listed:
• M. H. A. Davis
• M. R. Pistorius

## Abstract

For a given Markov process $X$ and survival function $\overline{H}$ on $\mathbb{R}^+$, the inverse first-passage time problem (IFPT) is to find a barrier function $b:\mathbb{R}^+\to[-\infty,+\infty]$ such that the survival function of the first-passage time \$\tau_b=\inf \{t\ge0:X(t)

## Suggested Citation

• M. H. A. Davis & M. R. Pistorius, 2013. "Explicit solution of an inverse first-passage time problem for L\'{e}vy processes and counterparty credit risk," Papers 1306.2719, arXiv.org, revised Sep 2015.
• Handle: RePEc:arx:papers:1306.2719
as

File URL: http://arxiv.org/pdf/1306.2719

## References listed on IDEAS

as
1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
2. Christophette Blanchet-Scalliet & Fr'ed'eric Patras, 2008. "Counterparty risk valuation for CDS," Papers 0807.0309, arXiv.org.
Full references (including those not matched with items on IDEAS)

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