In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative Lévy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized scale functions. For step weight functions, the Laplace transforms can be further expressed in terms of scale functions.

中文翻译：

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盈余会接近历史高位多长时间？

在本文中，我们发现频谱负Lévy盈余过程的加权占用时间的Laplace变换花费低于其运行最大值，直到第一个出口时间。结果用广义尺度函数表示。对于阶跃权重函数，可以按比例函数进一步表示拉普拉斯变换。