The Parisian and ultimate drawdowns of Lévy insurance models

Shu Li and Xiaowen Zhou

Insurance: Mathematics and Economics, 2022, vol. 107, issue C, 140-160

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.

Keywords: Parisian drawdown; Ultimate drawdown; Lévy process; Scale functions; Exit identities; Drawdown insurance (search for similar items in EconPapers)
JEL-codes: C02 G22 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:107:y:2022:i:c:p:140-160

DOI: 10.1016/j.insmatheco.2022.08.004

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