{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T08:43:34Z","timestamp":1778748214708,"version":"3.51.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,12,3]],"date-time":"2011-12-03T00:00:00Z","timestamp":1322870400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2012,2]]},"DOI":"10.1007\/s00186-011-0376-z","type":"journal-article","created":{"date-parts":[[2011,12,3]],"date-time":"2011-12-03T14:16:53Z","timestamp":1322921813000},"page":"83-100","source":"Crossref","is-referenced-by-count":41,"title":["Stochastic differential portfolio games for an insurer in a jump-diffusion risk process"],"prefix":"10.1007","volume":"75","author":[{"given":"Xiang","family":"Lin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tak Kuen","family":"Siu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,12,3]]},"reference":[{"issue":"1","key":"376_CR1","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1239\/jap\/1014842273","volume":"37","author":"S Browne","year":"2000","unstructured":"Browne S (2000) Stochastic differential portfolio games. J Appl Probab 37(1): 126\u2013147","journal-title":"J Appl Probab"},{"key":"376_CR2","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/S0167-6687(00)00055-X","volume":"27","author":"A Cairns","year":"2000","unstructured":"Cairns A (2000) A discussion of parameter and model uncertainty in insurance. Insur Math Econ 27: 313\u2013330","journal-title":"Insur Math Econ"},{"key":"376_CR3","volume-title":"Model risk. Quantitative strategies research notes","author":"E Derman","year":"1996","unstructured":"Derman E (1996) Model risk. Quantitative strategies research notes. Goldman Sachs, New York"},{"key":"376_CR4","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0167-6687(91)90023-Q","volume":"10","author":"F Dufresne","year":"1991","unstructured":"Dufresne F, Gerber HU (1991) Risk theory for the compound Poisson process that is perturbed by diffusion. Insur Math Econ 10: 51\u201359","journal-title":"Insur Math Econ"},{"key":"376_CR5","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1080\/00207727208920209","volume":"2","author":"RJ Elliott","year":"1972","unstructured":"Elliott RJ (1972) A max-min differential game in Hilbert space. Int J Syst Sci 2: 427\u2013433","journal-title":"Int J Syst Sci"},{"issue":"1","key":"376_CR6","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1137\/0314006","volume":"14","author":"RJ Elliott","year":"1976","unstructured":"Elliott RJ (1976) The existence of value in stochastic differential games. SIAM J Control Optim 14(1): 85\u201394","journal-title":"SIAM J Control Optim"},{"key":"376_CR7","unstructured":"Elliott RJ, Kalton NJ (1972) The existence of value in differential games. Mem Am Math Soc 126"},{"key":"376_CR8","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s11009-008-9085-3","volume":"11","author":"RJ Elliott","year":"2009","unstructured":"Elliott RJ, Siu TK (2009) Robust optimal portfolio choice under Markovian regime-switching model. Methodol Comput Appl Probab 11: 145\u2013157","journal-title":"Methodol Comput Appl Probab"},{"key":"376_CR9","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s10479-008-0448-5","volume":"176","author":"RJ Elliott","year":"2010","unstructured":"Elliott RJ, Siu TK (2010) On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy. Ann Oper Res 176: 271\u2013291","journal-title":"Ann Oper Res"},{"key":"376_CR10","doi-asserted-by":"crossref","first-page":"643","DOI":"10.2307\/1884324","volume":"25","author":"D Ellsberg","year":"1961","unstructured":"Ellsberg D (1961) Risk ambiguity and savage axioms. Q. J. Econ 25: 643\u2013669","journal-title":"Q. J. Econ"},{"key":"376_CR11","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1512\/iumj.1984.33.33040","volume":"33","author":"LC Evans","year":"1984","unstructured":"Evans LC, Souganidis PE (1984) Differential games and representation formulas for solutions of Hamilton- Jacobi-Isaacs equations. Indiana Univ Math J 33: 773\u2013797","journal-title":"Indiana Univ Math J"},{"key":"376_CR12","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/0022-247X(61)90009-9","volume":"3","author":"WH Fleming","year":"1961","unstructured":"Fleming WH (1961) The convergence problem for differential games. J Math Anal Appl 3: 102\u2013116","journal-title":"J Math Anal Appl"},{"key":"376_CR13","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1512\/iumj.1989.38.38015","volume":"38","author":"WH Fleming","year":"1989","unstructured":"Fleming WH, Souganidis PE (1989) On the existence of value function of two-player, zero-sum stochastic differential games. Indiana Univ Math J 38: 293\u2013314","journal-title":"Indiana Univ Math J"},{"key":"376_CR14","volume-title":"Differential Games","author":"A Friedman","year":"1971","unstructured":"Friedman A (1971) Differential Games. Wiley, New York"},{"key":"376_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. Springer, New York"},{"key":"376_CR16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0304-4068(89)90018-9","volume":"18","author":"I Giboa","year":"1989","unstructured":"Giboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J Math Econ 18: 141\u2013153","journal-title":"J Math Econ"},{"key":"376_CR17","volume-title":"Robustness","author":"LP Hansen","year":"2009","unstructured":"Hansen LP, Sargent TJ (2009) Robustness. Princeton University Press, Princeton, NJ"},{"key":"376_CR18","volume-title":"Differential Games","author":"R Isaacs","year":"1965","unstructured":"Isaacs R (1965) Differential Games. Wiley, New York"},{"key":"376_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00245-004-0818-6","volume":"52","author":"H Kaise","year":"2005","unstructured":"Kaise H, Sheu SJ (2005) Differential games of inf-sup type and Isaacs equations. Appl Math Optim 52: 1\u201322","journal-title":"Appl Math Optim"},{"key":"376_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.insmatheco.2004.10.004","volume":"36","author":"R Korn","year":"2005","unstructured":"Korn R (2005) Worst-case scenario investment for insurers. Insur Math Econom 36: 1\u201311","journal-title":"Insur Math Econom"},{"key":"376_CR21","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s00186-005-0444-3","volume":"62","author":"R Korn","year":"2005","unstructured":"Korn R, Menkens O (2005) Worst-case scenario portfolio optimization: A new stochastic control approach. Math Methods Oper Res 62: 123\u2013140","journal-title":"Math Methods Oper Res"},{"issue":"6","key":"376_CR22","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1137\/060657145","volume":"46","author":"R Korn","year":"2007","unstructured":"Korn R, Steffensen M (2007) On worst-case portfolio optimization. SIAM J Control Optim 46(6): 2013\u20132030","journal-title":"SIAM J Control Optim"},{"key":"376_CR23","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1142\/S0219024902001407","volume":"5","author":"R Korn","year":"2002","unstructured":"Korn R, Wilmott P (2002) Optimal portfolios under the threat of a crash. Int J Theor Appl Finance 5: 171\u2013187","journal-title":"Int J Theor Appl Finance"},{"issue":"6","key":"376_CR24","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1093\/rfs\/hhm035","volume":"21","author":"M Leippold","year":"2008","unstructured":"Leippold M, Trojani F, Vanini P (2008) Learning and asset prices under ambiguous information. Rev Financ Stud 21(6): 2565\u20132597","journal-title":"Rev Financ Stud"},{"key":"376_CR25","doi-asserted-by":"crossref","first-page":"77","DOI":"10.2307\/2975974","volume":"7","author":"H Markowitz","year":"1952","unstructured":"Markowitz H (1952) Portfolio selection. J Finance 7: 77\u201391","journal-title":"J Finance"},{"issue":"4","key":"376_CR26","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1080\/17442500701655408","volume":"80","author":"S Mataramvura","year":"2008","unstructured":"Mataramvura S, Oksendal B (2008) Risk minimizing and HJBI equations for stochastic differential games. Stoch Int J Probab Stoch Process 80(4): 317\u2013337","journal-title":"Stoch Int J Probab Stoch Process"},{"key":"376_CR27","doi-asserted-by":"crossref","first-page":"247","DOI":"10.2307\/1926560","volume":"51","author":"RC Merton","year":"1969","unstructured":"Merton RC (1969) Life-time portfolio selection under uncertainty: the continuous-time case. Rev Econ Stat 51: 247\u2013257","journal-title":"Rev Econ Stat"},{"key":"376_CR28","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/0022-0531(71)90038-X","volume":"3","author":"RC Merton","year":"1971","unstructured":"Merton RC (1971) Optimal consumption and portfolio rules in a continuous-time model. J Econ Theory 3: 373\u2013413","journal-title":"J Econ Theory"},{"key":"376_CR29","unstructured":"Oksendal B, Sulem A (2007) A game theoretic approach to martingale measures in incomplete markets. University of Oslo and INRIA. Preprint"},{"key":"376_CR30","first-page":"291","volume":"58","author":"MC Quenez","year":"2004","unstructured":"Quenez MC (2004) Optimal portfolio in a multiple priors model. Prog Probab 58: 291\u2013321","journal-title":"Prog Probab"},{"issue":"3","key":"376_CR31","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1111\/j.1467-9965.2006.00281.x","volume":"16","author":"C Roma","year":"2006","unstructured":"Roma C (2006) Model uncertainty and its impact on the pricing of derivative instruments. Math Fiance 16(3): 519\u2013547","journal-title":"Math Fiance"},{"key":"376_CR32","volume-title":"Stochastic control in insurance","author":"H Schmidli","year":"2008","unstructured":"Schmidli H (2008) Stochastic control in insurance. Springer, London"},{"key":"376_CR33","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.insmatheco.2010.09.006","volume":"48","author":"M Taksar","year":"2011","unstructured":"Taksar M, Zeng XD (2011) Optimal non-proportional reinsurance control and stochastic differential games. Insur Math Econ 48: 64\u201371","journal-title":"Insur Math Econ"},{"key":"376_CR34","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1137\/0305009","volume":"5","author":"P Varaiya","year":"1967","unstructured":"Varaiya P (1967) The existence of solution to a differential game. SIAM J Control Optim 5: 153\u2013162","journal-title":"SIAM J Control Optim"},{"key":"376_CR35","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/j.insmatheco.2005.06.009","volume":"37","author":"HL Yang","year":"2005","unstructured":"Yang HL, Zhang LH (2005) Optimal investment for insurer with jump-diffusion risk process. Insur Math Econ 37: 615\u2013634","journal-title":"Insur Math Econ"},{"issue":"2","key":"376_CR36","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1239\/jap\/1276784895","volume":"47","author":"XD Zeng","year":"2010","unstructured":"Zeng XD (2010) Stochastic differential reinsurance games. J Appl Probab 47(2): 335\u2013349","journal-title":"J Appl Probab"},{"key":"376_CR37","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.insmatheco.2009.04.001","volume":"45","author":"X Zhang","year":"2009","unstructured":"Zhang X, Siu TK (2009) Optimal investment and reinsurance of an insurer with model uncertainty. Insur Math Econ 45: 81\u201388","journal-title":"Insur Math Econ"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-011-0376-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00186-011-0376-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-011-0376-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T10:33:30Z","timestamp":1558607610000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00186-011-0376-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,3]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["376"],"URL":"https:\/\/doi.org\/10.1007\/s00186-011-0376-z","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"value":"1432-2994","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12,3]]}}}