Abstract
In this paper, inspired by the ideas of Parisian ruin and ultimate bankruptcy, we introduce two new stopping times for the (general) drawdown process, namely, the Parisian drawdown and ultimate drawdown under the exponential implementation delays. We provide quantitative analysis of their distributional properties of interest through the generalized scale functions, whose properties are examined as well. We then discuss their relationships with the existing results on exit times and occupation times as the application of our main results. Another application in the fair market valuation of drawdown insurance is also presented and illustrated in a numerical example.
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