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Time Reversal and Last Passage Time of Diffusions with Applications to Credit Risk Management

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  • Masahiko Egami
  • Rusudan Kevkhishvili

Abstract

We study time reversal, last passage time, and $h$-transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to an arbitrary level and analyze the distribution of the time left until killing after the last passage time. With these tools, we develop a new risk management framework for companies based on the leverage process (the ratio of a company asset process over its debt) and its corresponding alarming level. We also suggest how a company can determine the alarming level for the leverage process by constructing a relevant optimization problem.

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  • Masahiko Egami & Rusudan Kevkhishvili, 2017. "Time Reversal and Last Passage Time of Diffusions with Applications to Credit Risk Management," Papers 1701.04565, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1701.04565
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    References listed on IDEAS

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    1. Jin‐Chuan Duan, 2000. "Correction: Maximum Likelihood Estimation Using Price Data of the Derivative Contract (Mathematical Finance 1994, 4/2, 155–167)," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 461-462, October.
    2. Jin‐Chuan Duan, 1994. "Maximum Likelihood Estimation Using Price Data Of The Derivative Contract," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 155-167, April.
    3. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
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