No Cover Image

Journal article 36 views 2 downloads

Optimal periodic strategies with dividends payable from gains only

Eric C.K. Cheung Orcid Logo, Kob Liu Orcid Logo, Jae-Kyung Woo Orcid Logo, Jiannan Zhang Orcid Logo, Dan Zhu Orcid Logo

Insurance: Mathematics and Economics, Volume: 127, Start page: 103203

Swansea University Author: Kob Liu Orcid Logo

  • 71224.VOR.pdf

    PDF | Version of Record

    © 2025 The Author(s). This is an open access article under the CC BY-NC-ND license.

    Download (3.45MB)

Check full text

DOI (Published version): 10.1016/j.insmatheco.2025.103203

Abstract

In this paper, we consider the compound Poisson insurance risk model and analyze the optimal dividend strategy (that maximizes the expected present value of dividend payments until ruin) when dividends can only be paid periodically as lump sums. If one makes the usual assumption that dividends can b...

Full description

Published in: Insurance: Mathematics and Economics
ISSN: 0167-6687 1873-5959
Published: Elsevier BV 2026
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa71224
first_indexed 2026-01-09T13:15:49Z
last_indexed 2026-01-10T05:26:36Z
id cronfa71224
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2026-01-09T13:17:59.6894072</datestamp><bib-version>v2</bib-version><id>71224</id><entry>2026-01-09</entry><title>Optimal periodic strategies with dividends payable from gains only</title><swanseaauthors><author><sid>f3a9b352db430540db04208ab15e0e40</sid><ORCID>0000-0002-3072-0805</ORCID><firstname>Kob</firstname><surname>Liu</surname><name>Kob Liu</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2026-01-09</date><deptcode>MACS</deptcode><abstract>In this paper, we consider the compound Poisson insurance risk model and analyze the optimal dividend strategy (that maximizes the expected present value of dividend payments until ruin) when dividends can only be paid periodically as lump sums. If one makes the usual assumption that dividends can be paid from the available surplus, then the optimal strategies are often of band or barrier type, resulting in a ruin probability of one (e.g. Albrecher et al. (2011a)). As opposed to such an assumption, we propose that dividends can only be paid from a certain fraction of the gains (i.e. positive increment of the process between successive dividend decision times), and such a constraint allows the surplus process to have a positive survival probability. Some theoretical properties of the value function and the optimal strategy are derived in connection to the Bellman equation. These properties suggest that a bang-bang type of control can be a candidate for the optimal strategy, where dividend is paid at the highest possible amount as long as the surplus is high enough. The dividend function under the candidate strategy is subsequently derived under exponential inter-observation times and claims with a rational Laplace transform, and we also provide specific numerical examples with (mixed) exponential claims where the proposed strategy is optimal in such cases.</abstract><type>Journal Article</type><journal>Insurance: Mathematics and Economics</journal><volume>127</volume><journalNumber/><paginationStart>103203</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0167-6687</issnPrint><issnElectronic>1873-5959</issnElectronic><keywords>Periodic observation; Optimal dividends; Threshold strategy; Bellman equation</keywords><publishedDay>1</publishedDay><publishedMonth>3</publishedMonth><publishedYear>2026</publishedYear><publishedDate>2026-03-01</publishedDate><doi>10.1016/j.insmatheco.2025.103203</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics and Computer Science School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>MACS</DepartmentCode><institution>Swansea University</institution><apcterm>Another institution paid the OA fee</apcterm><funders>Australian Research Council&#x2019;s Discovery Project (DP200100615)</funders><projectreference/><lastEdited>2026-01-09T13:17:59.6894072</lastEdited><Created>2026-01-09T13:06:05.7337033</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Eric C.K.</firstname><surname>Cheung</surname><orcid>0000-0002-7693-5123</orcid><order>1</order></author><author><firstname>Kob</firstname><surname>Liu</surname><orcid>0000-0002-3072-0805</orcid><order>2</order></author><author><firstname>Jae-Kyung</firstname><surname>Woo</surname><orcid>0000-0002-3661-0711</orcid><order>3</order></author><author><firstname>Jiannan</firstname><surname>Zhang</surname><orcid>0000-0002-5695-2452</orcid><order>4</order></author><author><firstname>Dan</firstname><surname>Zhu</surname><orcid>0000-0003-1487-2232</orcid><order>5</order></author></authors><documents><document><filename>71224__35944__c9a16eae845940ac9415665f993652d4.pdf</filename><originalFilename>71224.VOR.pdf</originalFilename><uploaded>2026-01-09T13:13:46.9706528</uploaded><type>Output</type><contentLength>3621561</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><documentNotes>&#xA9; 2025 The Author(s). This is an open access article under the CC BY-NC-ND license.</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>http://creativecommons.org/licenses/by-nc-nd/4.0/</licence></document></documents><OutputDurs/></rfc1807>
spelling 2026-01-09T13:17:59.6894072 v2 71224 2026-01-09 Optimal periodic strategies with dividends payable from gains only f3a9b352db430540db04208ab15e0e40 0000-0002-3072-0805 Kob Liu Kob Liu true false 2026-01-09 MACS In this paper, we consider the compound Poisson insurance risk model and analyze the optimal dividend strategy (that maximizes the expected present value of dividend payments until ruin) when dividends can only be paid periodically as lump sums. If one makes the usual assumption that dividends can be paid from the available surplus, then the optimal strategies are often of band or barrier type, resulting in a ruin probability of one (e.g. Albrecher et al. (2011a)). As opposed to such an assumption, we propose that dividends can only be paid from a certain fraction of the gains (i.e. positive increment of the process between successive dividend decision times), and such a constraint allows the surplus process to have a positive survival probability. Some theoretical properties of the value function and the optimal strategy are derived in connection to the Bellman equation. These properties suggest that a bang-bang type of control can be a candidate for the optimal strategy, where dividend is paid at the highest possible amount as long as the surplus is high enough. The dividend function under the candidate strategy is subsequently derived under exponential inter-observation times and claims with a rational Laplace transform, and we also provide specific numerical examples with (mixed) exponential claims where the proposed strategy is optimal in such cases. Journal Article Insurance: Mathematics and Economics 127 103203 Elsevier BV 0167-6687 1873-5959 Periodic observation; Optimal dividends; Threshold strategy; Bellman equation 1 3 2026 2026-03-01 10.1016/j.insmatheco.2025.103203 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee Australian Research Council’s Discovery Project (DP200100615) 2026-01-09T13:17:59.6894072 2026-01-09T13:06:05.7337033 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Eric C.K. Cheung 0000-0002-7693-5123 1 Kob Liu 0000-0002-3072-0805 2 Jae-Kyung Woo 0000-0002-3661-0711 3 Jiannan Zhang 0000-0002-5695-2452 4 Dan Zhu 0000-0003-1487-2232 5 71224__35944__c9a16eae845940ac9415665f993652d4.pdf 71224.VOR.pdf 2026-01-09T13:13:46.9706528 Output 3621561 application/pdf Version of Record true © 2025 The Author(s). This is an open access article under the CC BY-NC-ND license. true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title Optimal periodic strategies with dividends payable from gains only
spellingShingle Optimal periodic strategies with dividends payable from gains only
Kob Liu
title_short Optimal periodic strategies with dividends payable from gains only
title_full Optimal periodic strategies with dividends payable from gains only
title_fullStr Optimal periodic strategies with dividends payable from gains only
title_full_unstemmed Optimal periodic strategies with dividends payable from gains only
title_sort Optimal periodic strategies with dividends payable from gains only
author_id_str_mv f3a9b352db430540db04208ab15e0e40
author_id_fullname_str_mv f3a9b352db430540db04208ab15e0e40_***_Kob Liu
author Kob Liu
author2 Eric C.K. Cheung
Kob Liu
Jae-Kyung Woo
Jiannan Zhang
Dan Zhu
format Journal article
container_title Insurance: Mathematics and Economics
container_volume 127
container_start_page 103203
publishDate 2026
institution Swansea University
issn 0167-6687
1873-5959
doi_str_mv 10.1016/j.insmatheco.2025.103203
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 compound Poisson insurance risk model and analyze the optimal dividend strategy (that maximizes the expected present value of dividend payments until ruin) when dividends can only be paid periodically as lump sums. If one makes the usual assumption that dividends can be paid from the available surplus, then the optimal strategies are often of band or barrier type, resulting in a ruin probability of one (e.g. Albrecher et al. (2011a)). As opposed to such an assumption, we propose that dividends can only be paid from a certain fraction of the gains (i.e. positive increment of the process between successive dividend decision times), and such a constraint allows the surplus process to have a positive survival probability. Some theoretical properties of the value function and the optimal strategy are derived in connection to the Bellman equation. These properties suggest that a bang-bang type of control can be a candidate for the optimal strategy, where dividend is paid at the highest possible amount as long as the surplus is high enough. The dividend function under the candidate strategy is subsequently derived under exponential inter-observation times and claims with a rational Laplace transform, and we also provide specific numerical examples with (mixed) exponential claims where the proposed strategy is optimal in such cases.
published_date 2026-03-01T05:33:33Z
_version_ 1856805811952549888
score 11.096027

Similar Items