Time Reversal and Last Passage Time of Diffusions with Applications to Credit Risk Management
Mathematical Finance
2019-02-28 v6
Abstract
We study time reversal, last passage time, and -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.
Keywords
Cite
@article{arxiv.1701.04565,
title = {Time Reversal and Last Passage Time of Diffusions with Applications to Credit Risk Management},
author = {Masahiko Egami and Rusudan Kevkhishvili},
journal= {arXiv preprint arXiv:1701.04565},
year = {2019}
}