This article develops a new risk management framework for companies on the basis of the leverage process (a ratio of company asset value over its debt). We approach this task by time reversal, last passage time, and the h-transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to a certain alarming level and analyze the distribution of the time left until killing after the last passage time to that level. We then apply these results to the leverage process of the company. Finally, we suggest how a company should determine the aforementioned alarming level . Specifically, we construct a relevant optimization problem and derive an optimal alarming level as its solution .
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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