This paper develops a risk management framework for companies, based on the leverage process (a ratio of company asset value over its debt) by analyzing the characteristics of general linear diffusions with killing. We approach this issue by time reversal, last passage time, and h-transform of linear diffusions. For such processes, we derive the probability density of the last passage time to a certain alarming level and the distribution of the time left until killing after the last passage time. We apply these results to the leverage process of the company. Finally, we suggest how a company should specify that abovementioned alarming level for the leverage process by solving an optimization problem.
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