This article develops a new risk management framework for companies based onthe leverage process (a ratio of company asset value over its debt). Weapproach this task by time reversal, last passage time, and $h$-transform oflinear diffusions. For general diffusions with killing, we obtain theprobability density of the last passage time to a certain alarming level, andanalyze the distribution of the time left until killing after the last passagetime to that level. We then apply these results to the leverage process of thecompany. Finally, we suggest how a company should determine the aforementionedalarming level. More specifically, we construct a relevant optimization problemand derive an optimal alarming level as its solution.
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机译：本文为基于杠杆流程（公司资产价值与债务）的比率为公司开发了新的风险管理框架。武器按时间逆转，最后一段时间和$ h $ -transform的武器这项任务。对于杀戮的一般扩散，我们获得了最后一段时间的可Probiability密度到一定的警报水平，并分析了剩余时间的分布，直到在最后一次偏航时间到达那个水平后杀死。然后，我们将这些结果应用于Company的杠杆过程。最后，我们建议公司应该如何确定上述身份化水平。更具体地说，我们构建了相关的优化问题和获得最佳警报级别作为其解决方案。
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