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On the analysis of deep drawdowns for the Lévy insurance risk model

On the analysis of deep drawdowns for the Lévy insurance risk model
On the analysis of deep drawdowns for the Lévy insurance risk model

In this paper, we study the magnitude and the duration of deep drawdowns for the Lévy insurance risk model through the characterization of the Laplace transform of a related stopping time. Relying on a temporal approximation approach (e.g., Li et al. (2018)), the proposed methodology allows for a unified treatment of processes with bounded and unbounded variation paths whereas these two cases used to be treated separately. In particular, we extend the results of Landriault et al. (2017) and Surya (2019). We later analyze certain limiting cases of our main results where consistency with some known drawdown results in the literature will be shown.

Drawdown duration, Drawdown magnitude, Drawdown process, Lévy insurance risk processes, Scale functions
0167-6687
147-155
Landriault, David
cb59d585-94dd-4a67-a4b1-18a1baeb0505
Li, Bin
b96a645c-851a-4861-b2da-c531001e51d4
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b
Landriault, David
cb59d585-94dd-4a67-a4b1-18a1baeb0505
Li, Bin
b96a645c-851a-4861-b2da-c531001e51d4
Lkabous, Mohamed Amine
c511ddd2-2517-471b-bd73-8d8b7ab74a1b

Landriault, David, Li, Bin and Lkabous, Mohamed Amine (2021) On the analysis of deep drawdowns for the Lévy insurance risk model. Insurance: Mathematics and Economics, 100, 147-155. (doi:10.1016/j.insmatheco.2021.05.004).

Record type: Review

Abstract

In this paper, we study the magnitude and the duration of deep drawdowns for the Lévy insurance risk model through the characterization of the Laplace transform of a related stopping time. Relying on a temporal approximation approach (e.g., Li et al. (2018)), the proposed methodology allows for a unified treatment of processes with bounded and unbounded variation paths whereas these two cases used to be treated separately. In particular, we extend the results of Landriault et al. (2017) and Surya (2019). We later analyze certain limiting cases of our main results where consistency with some known drawdown results in the literature will be shown.

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On the analysis of deep drawdowns for the Lévy insurance risk model - Accepted Manuscript
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Accepted/In Press date: 12 May 2021
e-pub ahead of print date: 20 May 2021
Published date: September 2021
Additional Information: Funding Information: Support from grants from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged by David Landriault and Bin Li (grant numbers 341316 and 05828 , respectively). Support from the Canada Research Chairs Program is gratefully acknowledged by David Landriault. Publisher Copyright: © 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords: Drawdown duration, Drawdown magnitude, Drawdown process, Lévy insurance risk processes, Scale functions

Identifiers

Local EPrints ID: 451055
URI: http://eprints.soton.ac.uk/id/eprint/451055
ISSN: 0167-6687
PURE UUID: 2160e767-8058-4f26-9613-bec71ad0558a

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Date deposited: 03 Sep 2021 16:44
Last modified: 18 Mar 2024 05:27

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Contributors

Author: David Landriault
Author: Bin Li

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