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Optimal dividend policy with self-exciting claims in the Gamma–Omega model
Finance Research Letters, Start page: 106162
Swansea University Author: Kob Liu
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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...
Published in: | Finance Research Letters |
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ISSN: | 1544-6123 |
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Elsevier BV
2024
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URI: | https://cronfa.swan.ac.uk/Record/cronfa67782 |
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v2 67782 2024-09-25 Optimal dividend policy with self-exciting claims in the Gamma–Omega model f3a9b352db430540db04208ab15e0e40 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 0 106162 Elsevier BV 1544-6123 Dynamic programming, self-exciting Hawkes process, Gamma-Omega model, optimaldividend strategy 24 9 2024 2024-09-24 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 2024-09-25T11:11:15.0814615 2024-09-25T10:57:40.6455244 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Kob Liu 1 Zhuo Jin 2 Shuanming Li 0000-0003-4102-4618 3 67782__31452__bbce188589034571a465d07b5532f341.pdf 67782.AAM.pdf 2024-09-25T11:08:14.6026294 Output 1468042 application/pdf Accepted Manuscript true true eng |
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 |
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f3a9b352db430540db04208ab15e0e40 |
author_id_fullname_str_mv |
f3a9b352db430540db04208ab15e0e40_***_Kob Liu |
author |
Kob Liu |
author2 |
Kob Liu Zhuo Jin Shuanming Li |
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Finance Research Letters |
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106162 |
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1544-6123 |
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10.1016/j.frl.2024.106162 |
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Elsevier BV |
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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 |
2024-09-24T11:13:35Z |
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1811162559076630528 |
score |
11.028798 |