{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T12:56:59Z","timestamp":1774443419556,"version":"3.50.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,2,16]],"date-time":"2024-02-16T00:00:00Z","timestamp":1708041600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,2,16]],"date-time":"2024-02-16T00:00:00Z","timestamp":1708041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201311"],"award-info":[{"award-number":["12201311"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Founding of the Jiangsu Higher Education Institutions of China","award":["22KJB110021"],"award-info":[{"award-number":["22KJB110021"]}]},{"name":"Natural Science Founding of the Jiangsu Higher Education Institutions of China","award":["12101299"],"award-info":[{"award-number":["12101299"]}]},{"name":"Natural Science Foundation in Jiangsu","award":["BK20210668"],"award-info":[{"award-number":["BK20210668"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s10479-024-05844-6","type":"journal-article","created":{"date-parts":[[2024,2,16]],"date-time":"2024-02-16T20:02:38Z","timestamp":1708113758000},"page":"441-467","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Stochastic differential reinsurance game for two competitive insurers with ambiguity-aversion under mean-variance premium principle"],"prefix":"10.1007","volume":"335","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5004-910X","authenticated-orcid":false,"given":"Yu","family":"Yuan","sequence":"first","affiliation":[]},{"given":"Kexin","family":"Wang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3080-6158","authenticated-orcid":false,"given":"Caibin","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,2,16]]},"reference":[{"issue":"1","key":"5844_CR1","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1162\/154247603322256774","volume":"1","author":"EW Anderson","year":"2003","unstructured":"Anderson, E. W., Hansen, L. P., & Sargent, T. J. (2003). A quartet of semigroups for model specification, robustness, prices of risk, and model detection. Journal of the European Economic Association, 1(1), 68\u2013123.","journal-title":"Journal of the European Economic Association"},{"key":"5844_CR2","first-page":"664","volume":"53","author":"L Bai","year":"2013","unstructured":"Bai, L., Cai, J., & Zhou, M. (2013). Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting. Insurance: Mathematics and Economics, 53, 664\u2013670.","journal-title":"Insurance: Mathematics and Economics"},{"issue":"10","key":"5844_CR3","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1080\/14697680902968005","volume":"10","author":"L Bai","year":"2010","unstructured":"Bai, L., Guo, J., & Zhang, H. (2010). Optimal excess-of-loss reinsurance and dividend payments with both transaction costs and taxes. Quantitative Finance, 10(10), 1163\u20131172.","journal-title":"Quantitative Finance"},{"issue":"2","key":"5844_CR4","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1016\/j.ejor.2021.04.046","volume":"296","author":"Y Bai","year":"2022","unstructured":"Bai, Y., Zhou, Z., Xiao, H., Gao, R., & Zhong, F. (2022). A hybrid stochastic differential reinsurance and investment game with bounded memory. European Journal of Operational Research, 296(2), 717\u2013737.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"5844_CR5","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1016\/j.ejor.2021.08.038","volume":"298","author":"I Baltas","year":"2022","unstructured":"Baltas, I., Dopierala, L., Kolodziejczyk, K., Szczepa\u0144ski, M., Weber, G. W., & Yannacopoulos, A. N. (2022). Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty. European Journal of Operational Research, 298(3), 1162\u20131174.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"5844_CR6","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/jofi.12106","volume":"69","author":"S Basak","year":"2014","unstructured":"Basak, S., & Makarov, D. (2014). Strategic asset allocation in money management. The Journal of finance, 69(1), 179\u2013217.","journal-title":"The Journal of finance"},{"issue":"8","key":"5844_CR7","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1016\/j.automatica.2014.05.033","volume":"50","author":"A Bensoussan","year":"2014","unstructured":"Bensoussan, A., Siu, C. C., Yam, S. C. P., & Yang, H. (2014). A class of non-zero-sum stochastic differential investment and reinsurance games. Automatica, 50(8), 2025\u20132037.","journal-title":"Automatica"},{"key":"5844_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10479-021-04317-4","volume":"307","author":"J Bi","year":"2021","unstructured":"Bi, J., Cai, J., & Zeng, Y. (2021). Equilibrium reinsurance-investment strategies with partial information and common shock dependence. Annals of Operations Research, 307, 1\u201324.","journal-title":"Annals of Operations Research"},{"key":"5844_CR9","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1017\/S0515036100009557","volume":"1","author":"K Borch","year":"1960","unstructured":"Borch, K. (1960). Reciprocal reinsurance treaties. ASTIN Bulletin, 1, 171\u2013191.","journal-title":"ASTIN Bulletin"},{"key":"5844_CR10","first-page":"1","volume":"95","author":"M Brachetta","year":"2020","unstructured":"Brachetta, M., & Ceci, C. (2020). A BSDE-based approach for the optimal reinsurance problem under partial information. Insurance: Mathematics and Economics, 95, 1\u201316.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR11","first-page":"253","volume":"71","author":"L Chen","year":"2016","unstructured":"Chen, L., Qian, L., Shen, Y., & Wang, W. (2016). Constrained investment-reinsurance optimization with regime switching under variance premium principle. Insurance: Mathematics and Economics, 71, 253\u2013267.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR12","first-page":"27","volume":"92","author":"Z Chen","year":"2020","unstructured":"Chen, Z., & Yang, P. (2020). Robust optimal reinsurance-investment strategy with price jumps and correlated claims. Insurance: Mathematics and Economics, 92, 27\u201346.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.fss.2020.04.019","volume":"409","author":"H Galindo","year":"2021","unstructured":"Galindo, H., Gallardo, J. M., & Jim\u00e9nez-Losada, A. (2021). A real Shapley value for cooperative games with fuzzy characteristic function. Fuzzy Sets and Systems, 409, 1\u201314.","journal-title":"Fuzzy Sets and Systems"},{"key":"5844_CR14","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.fss.2019.10.001","volume":"398","author":"JM Gallardo","year":"2020","unstructured":"Gallardo, J. M., & Jim\u00e9nez-Losada, A. (2020). A characterization of the Shapley value for cooperative games with fuzzy characteristic function. Fuzzy Sets and Systems, 398, 98\u2013111.","journal-title":"Fuzzy Sets and Systems"},{"key":"5844_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-9058-9","volume-title":"Aspects of risk theory","author":"J Grandell","year":"1991","unstructured":"Grandell, J. (1991). Aspects of risk theory. New York: Springer."},{"key":"5844_CR16","first-page":"63","volume":"89","author":"G Guan","year":"2019","unstructured":"Guan, G., & Liang, Z. (2019). Robust optimal reinsurance and investment strategies for an AAI with multiple risks. Insurance: Mathematics and Economics, 89, 63\u201378.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR17","first-page":"1","volume":"2","author":"X Han","year":"2020","unstructured":"Han, X., Liang, Z., & Young, V. R. (2020). Optimal reinsurance strategy to minimize the probability of drawdown under a mean-variance premium principle. Scandinavian Actuarial Journal, 2, 1\u201325.","journal-title":"Scandinavian Actuarial Journal"},{"issue":"3","key":"5844_CR18","doi-asserted-by":"crossref","first-page":"2495","DOI":"10.1007\/s00245-020-09714-y","volume":"84","author":"X Han","year":"2021","unstructured":"Han, X., Liang, Z., Yuen, K. C., & Yuan, Y. (2021). Minimizing the probability of absolute ruin under ambiguity aversion. Applied Mathematics and Optimization, 84(3), 2495\u20132525.","journal-title":"Applied Mathematics and Optimization"},{"issue":"1","key":"5844_CR19","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1017\/apr.2018.7","volume":"50","author":"H Hata","year":"2017","unstructured":"Hata, H., & Sheu, S. J. (2017). An optimal consumption and investment problem with partial information. Advances in Applied probability, 50(1), 131\u2013153.","journal-title":"Advances in Applied probability"},{"issue":"5","key":"5844_CR20","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1016\/j.cam.2018.05.060","volume":"344","author":"Y Huang","year":"2018","unstructured":"Huang, Y., Yao, O., Tang, L., & Zhou, J. (2018). Robust optimal investment and reinsurance problem for the product of the insurer\u2019s and the reinsurer\u2019s utilities. Journal of Computational and Applied Mathematics, 344(5), 532\u2013552.","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"7","key":"5844_CR21","doi-asserted-by":"crossref","first-page":"1550045","DOI":"10.1142\/S0219024915500454","volume":"18","author":"M Jeanblanc","year":"2015","unstructured":"Jeanblanc, M., Mastrolia, T., Possamai, D., & Reveillac, A. (2015). Utility maximization with random horizon: A BSDE approach. International Journal of Theoretical and Applied Finance, 18(7), 1550045.","journal-title":"International Journal of Theoretical and Applied Finance"},{"key":"5844_CR22","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10479-020-03757-8","volume":"295","author":"B Kalayci","year":"2020","unstructured":"Kalayci, B., \u00d6zmen, A., & Weber, G. W. (2020). Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS. Annals of Operations Research, 295, 183\u2013206.","journal-title":"Annals of Operations Research"},{"key":"5844_CR23","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10100-017-0508-5","volume":"27","author":"G Kara","year":"2019","unstructured":"Kara, G., \u00d6zmen, A., & Weber, G. W. (2019). Stability advances in robust portfolio optimization under parallelepiped uncertainty. Central European Journal of Operations Research, 27, 241\u2013261.","journal-title":"Central European Journal of Operations Research"},{"issue":"4","key":"5844_CR24","doi-asserted-by":"crossref","first-page":"253","DOI":"10.3934\/jdg.2020018","volume":"7","author":"E Kropat","year":"2020","unstructured":"Kropat, E., Weber, G. W., & Tirkolaee, E. B. (2020). Foundations of semialgebraic gene-environment networks. Journal of Dynamics and Games, 7(4), 253\u2013268.","journal-title":"Journal of Dynamics and Games"},{"key":"5844_CR25","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1016\/j.cam.2013.06.033","volume":"255","author":"D Li","year":"2014","unstructured":"Li, D., Rong, X., & Zhao, H. (2014). Optimal reinsurance-investment problem for maximizing the product of the insurer\u2019s and the reinsurer\u2019s utilities under a CEV model. Journal of Computational and Applied Mathematics, 255, 671\u2013683.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"5844_CR26","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1080\/03461238.2017.1309679","volume":"2","author":"D Li","year":"2018","unstructured":"Li, D., Zeng, Y., & Yang, H. (2018). Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps. Scandinavian Actuarial Journal, 2, 145\u2013171.","journal-title":"Scandinavian Actuarial Journal"},{"key":"5844_CR27","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.cam.2018.08.049","volume":"348","author":"S Luo","year":"2019","unstructured":"Luo, S., Wang, M., & Zhu, W. (2019). Maximizing a robust goal-reaching probability with penalization on ambiguity. Journal of Computational and Applied Mathematics, 348, 261\u2013281.","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"1","key":"5844_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/17442500802201425","volume":"81","author":"MA Morlais","year":"2009","unstructured":"Morlais, M. A. (2009). Utility maximization in a jump market model. Stochastics, 81(1), 1\u201327.","journal-title":"Stochastics"},{"key":"5844_CR29","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s00186-014-0472-y","volume":"80","author":"O Palanci","year":"2014","unstructured":"Palanci, O., Alparslan G\u00f6k, S. Z., & Weber, G. W. (2014). Cooperative games under bubbly uncertainty. Mathematical Methods of Operations Research, 80, 129\u2013137.","journal-title":"Mathematical Methods of Operations Research"},{"issue":"3","key":"5844_CR30","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1080\/10920277.2005.10596214","volume":"9","author":"SD Promislow","year":"2005","unstructured":"Promislow, S. D., & Young, V. (2005). Minimizing the probability of ruin when claims follow Brownian motion with drift. North American Actuarial Journal, 9(3), 110\u2013128.","journal-title":"North American Actuarial Journal"},{"issue":"5","key":"5844_CR31","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1016\/j.orl.2016.06.004","volume":"44","author":"CS Pun","year":"2016","unstructured":"Pun, C. S., Siu, C. C., & Wong, H. Y. (2016). Non-zero-sum reinsurance games subject to ambiguous correlations. Operations Research Letters, 44(5), 578\u2013586.","journal-title":"Operations Research Letters"},{"issue":"2","key":"5844_CR32","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1007\/s10479-020-03768-5","volume":"312","author":"E Savku","year":"2022","unstructured":"Savku, E., & Weber, G. W. (2022). Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market. Annals of Operations Research, 312(2), 1171\u20131196.","journal-title":"Annals of Operations Research"},{"key":"5844_CR33","first-page":"670","volume":"8","author":"CC Siu","year":"2017","unstructured":"Siu, C. C., Yam, S. C. P., Yang, H., & Zhao, H. (2017). A class of nonzero-sum investment and reinsurance games subject to systematic risks. Scandinavian Actuarial Journal, 8, 670\u2013707.","journal-title":"Scandinavian Actuarial Journal"},{"key":"5844_CR34","first-page":"58","volume":"75","author":"M Yan","year":"2017","unstructured":"Yan, M., Peng, F., & Zhang, S. (2017). A reinsurance and investment game between two insurance companies with the different opinions about some extra information. Insurance: Mathematics and Economics, 75, 58\u201370.","journal-title":"Insurance: Mathematics and Economics"},{"issue":"3","key":"5844_CR35","first-page":"615","volume":"37","author":"H Yang","year":"2005","unstructured":"Yang, H., & Zhang, L. (2005). Optimal investment for insurer with jump-diffusion risk process. Insurance: Mathematics and Economics, 37(3), 615\u2013634.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR36","doi-asserted-by":"crossref","first-page":"112769","DOI":"10.1016\/j.cam.2020.112769","volume":"374","author":"P Yang","year":"2020","unstructured":"Yang, P., Chen, Z., & Xu, Y. (2020). Time-consistent equilibrium reinsurance-investment strategy for n competitive insurers under a new interaction mechanism and a general investment framework. Journal of Computational and Applied Mathematics, 374, 112769.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"5844_CR37","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/j.ejor.2023.05.023","volume":"311","author":"Y Yuan","year":"2023","unstructured":"Yuan, Y., Han, X., Liang, Z., & Yuen, K. C. (2023). Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework. European Journal of Operational Research, 311, 581\u2013595.","journal-title":"European Journal of Operational Research"},{"key":"5844_CR38","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1080\/03461238.2021.1971756","volume":"4","author":"Y Yuan","year":"2022","unstructured":"Yuan, Y., Liang, Z., & Han, X. (2022). Robust reinsurance contract with asymmetric information in a stochastic Stackelberg differential game. Scandinavian Actuarial Journal, 4, 328\u2013355.","journal-title":"Scandinavian Actuarial Journal"},{"key":"5844_CR39","doi-asserted-by":"crossref","first-page":"114816","DOI":"10.1016\/j.cam.2022.114816","volume":"420","author":"Y Yuan","year":"2023","unstructured":"Yuan, Y., Liang, Z., & Han, X. (2023). Robust optimal reinsurance in minimizing the penalized expected time to reach a goal. Journal of Computational and Applied Mathematics, 420, 114816.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"5844_CR40","first-page":"1","volume":"64","author":"KC Yuen","year":"2015","unstructured":"Yuen, K. C., Liang, Z., & Zhou, M. (2015). Optimal proportional reinsurance with common shock dependence. Insurance: Mathematics and Economics, 64, 1\u201313.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR41","unstructured":"Yuen, K. C., & Wang, G. (2002). Comparing two models with dependent classes of business. In Proceedings of the 36th actuarial research conference, ARCH (Society of Actuaries). Columbus, Ohio, 22p."},{"key":"5844_CR42","first-page":"138","volume":"66","author":"Y Zeng","year":"2016","unstructured":"Zeng, Y., Li, D., & Gu, A. (2016). Robust equilibrium reinsurance-investment strategy for a mean-variance insurer in a model with jumps. Insurance: Mathematics and Economics, 66, 138\u2013152.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR43","first-page":"125","volume":"67","author":"X Zhang","year":"2016","unstructured":"Zhang, X., Meng, H., & Zeng, Y. (2016). Optimal investment and reinsurance strategies for insurers with generalized mean-variance premium principle and no-short selling. Insurance: Mathematics and Economics, 67, 125\u2013132.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR44","first-page":"504","volume":"53","author":"H Zhao","year":"2013","unstructured":"Zhao, H., Rong, X., & Zhao, Y. (2013). Optimal excess-of-loss reinsurance and investment problem for an insurer with jump\u2013diffusion risk process under the heston model. Insurance: Mathematics and Economics, 53, 504\u2013514.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR45","first-page":"77","volume":"67","author":"X Zheng","year":"2016","unstructured":"Zheng, X., Zhou, J., & Sun, Z. (2016). Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model. Insurance: Mathematics and Economics, 67, 77\u201387.","journal-title":"Insurance: Mathematics and Economics"},{"key":"5844_CR46","doi-asserted-by":"crossref","first-page":"112737","DOI":"10.1016\/j.cam.2020.112737","volume":"374","author":"J Zhu","year":"2020","unstructured":"Zhu, J., Guan, G., & Li, S. (2020). Time-consistent non-zero-sum stochastic differential reinsurance and investment game under default and volatility risks. Journal of Computational and Applied Mathematics, 374, 112737.","journal-title":"Journal of Computational and Applied Mathematics"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-024-05844-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-024-05844-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-024-05844-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T16:25:52Z","timestamp":1711729552000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-024-05844-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,16]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["5844"],"URL":"https:\/\/doi.org\/10.1007\/s10479-024-05844-6","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,16]]},"assertion":[{"value":"17 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}