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Optimal dividend policy with self-exciting claims in the Gamma–Omega model

Kob Liu Orcid Logo, Zhuo Jin, Shuanming Li Orcid Logo

Finance Research Letters, Volume: 69, Start page: 106162

Swansea University Author: Kob Liu Orcid Logo

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DOI (Published version): 10.1016/j.frl.2024.106162

Abstract

In this paper, we consider the optimal dividend policy for an insurance company under a contagious insurance market, where the occurrence of a claim can trigger sequent claims. This clustering effect is modelled by a self-exciting Hawkes process where the intensity of claims depends on its historica...

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Published in: Finance Research Letters
ISSN: 1544-6123
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa67782
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spelling 2024-10-18T14:01:37.3813241 v2 67782 2024-09-25 Optimal dividend policy with self-exciting claims in the Gamma–Omega model f3a9b352db430540db04208ab15e0e40 0000-0002-3072-0805 Kob Liu Kob Liu true false 2024-09-25 MACS In this paper, we consider the optimal dividend policy for an insurance company under a contagious insurance market, where the occurrence of a claim can trigger sequent claims. This clustering effect is modelled by a self-exciting Hawkes process where the intensity of claims depends on its historical path. In addition, we include the concept of bankruptcy to allow the insurance company to operate with a temporary negative surplus. The objective of the management is to obtain the optimal dividend strategy that maximises the expected discounted dividend payments until bankruptcy. The Hamilton–Jacobi–Bellman variational inequalities (HJBVIs) are derived rigorously. When claim sizes follow exponential distributions and the bankruptcy rate is a positive constant, the value function can be obtained based on the Gerber–Shiu penalty function and the optimal dividend barrier can be solved numerically. Finally, numerical examples are demonstrated to show the impact of key parameters on the optimal dividend strategy. Journal Article Finance Research Letters 69 106162 Elsevier BV 1544-6123 Dynamic programming, self-exciting Hawkes process, Gamma-Omega model, optimaldividend strategy 1 11 2024 2024-11-01 10.1016/j.frl.2024.106162 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansea University 2024-10-18T14:01:37.3813241 2024-09-25T10:57:40.6455244 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Kob Liu 0000-0002-3072-0805 1 Zhuo Jin 2 Shuanming Li 0000-0003-4102-4618 3 67782__32646__9bcee9c7c5af4fb9927d964ff36f594f.pdf 67782.VoR.pdf 2024-10-18T13:59:17.0556611 Output 926168 application/pdf Version of Record true © 2024 The Authors. This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Optimal dividend policy with self-exciting claims in the Gamma–Omega model
spellingShingle Optimal dividend policy with self-exciting claims in the Gamma–Omega model
Kob Liu
title_short Optimal dividend policy with self-exciting claims in the Gamma–Omega model
title_full Optimal dividend policy with self-exciting claims in the Gamma–Omega model
title_fullStr Optimal dividend policy with self-exciting claims in the Gamma–Omega model
title_full_unstemmed Optimal dividend policy with self-exciting claims in the Gamma–Omega model
title_sort Optimal dividend policy with self-exciting claims in the Gamma–Omega model
author_id_str_mv f3a9b352db430540db04208ab15e0e40
author_id_fullname_str_mv f3a9b352db430540db04208ab15e0e40_***_Kob Liu
author Kob Liu
author2 Kob Liu
Zhuo Jin
Shuanming Li
format Journal article
container_title Finance Research Letters
container_volume 69
container_start_page 106162
publishDate 2024
institution Swansea University
issn 1544-6123
doi_str_mv 10.1016/j.frl.2024.106162
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description In this paper, we consider the optimal dividend policy for an insurance company under a contagious insurance market, where the occurrence of a claim can trigger sequent claims. This clustering effect is modelled by a self-exciting Hawkes process where the intensity of claims depends on its historical path. In addition, we include the concept of bankruptcy to allow the insurance company to operate with a temporary negative surplus. The objective of the management is to obtain the optimal dividend strategy that maximises the expected discounted dividend payments until bankruptcy. The Hamilton–Jacobi–Bellman variational inequalities (HJBVIs) are derived rigorously. When claim sizes follow exponential distributions and the bankruptcy rate is a positive constant, the value function can be obtained based on the Gerber–Shiu penalty function and the optimal dividend barrier can be solved numerically. Finally, numerical examples are demonstrated to show the impact of key parameters on the optimal dividend strategy.
published_date 2024-11-01T12:05:36Z
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score 11.088929

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