Time reversal and last passage time of diffusions with applications to credit risk management

Masahiko Egami () and Rusudan Kevkhishvili ()
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Masahiko Egami: Kyoto University

Finance and Stochastics, 2020, vol. 24, issue 3, No 7, 795-825

Abstract: Abstract We study time reversal, last passage time and h $h$ -transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to an arbitrary level and analyse 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 optimisation problem.

Keywords: Time reversal; Linear diffusion; Last passage time; h $h$ -transform; Risk management; 60J60; 60J70 (search for similar items in EconPapers)
JEL-codes: G32 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00780-020-00423-6

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