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Article: A class of non-zero-sum stochastic differential investment and reinsurance games

TitleA class of non-zero-sum stochastic differential investment and reinsurance games
Authors
Issue Date2014
PublisherElsevier. The Journal's web site is located at http://www.elsevier.com/locate/automatica
Citation
Automatica, 2014, v. 50 n. 8, p. 2025-2037 How to Cite?
AbstractIn this article, we provide a systematic study on the non-zero-sum stochastic differential investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.
Persistent Identifierhttp://hdl.handle.net/10722/214573
ISSN
2015 Impact Factor: 3.635
2015 SCImago Journal Rankings: 4.315

 

DC FieldValueLanguage
dc.contributor.authorBensoussan, A-
dc.contributor.authorSiu, CC-
dc.contributor.authorYam, SCP-
dc.contributor.authorYang, H-
dc.date.accessioned2015-08-21T11:38:44Z-
dc.date.available2015-08-21T11:38:44Z-
dc.date.issued2014-
dc.identifier.citationAutomatica, 2014, v. 50 n. 8, p. 2025-2037-
dc.identifier.issn0005-1098-
dc.identifier.urihttp://hdl.handle.net/10722/214573-
dc.description.abstractIn this article, we provide a systematic study on the non-zero-sum stochastic differential investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.-
dc.languageeng-
dc.publisherElsevier. The Journal's web site is located at http://www.elsevier.com/locate/automatica-
dc.relation.ispartofAutomatica-
dc.rights© 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleA class of non-zero-sum stochastic differential investment and reinsurance games-
dc.typeArticle-
dc.identifier.emailYang, H: hlyang@hku.hk-
dc.identifier.authorityYang, H=rp00826-
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.automatica.2014.05.033-
dc.identifier.hkuros248421-
dc.identifier.volume50-
dc.identifier.issue8-
dc.identifier.spage2025-
dc.identifier.epage2037-
dc.publisher.placeUnited Kingdom-

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