Optimal non-proportional reinsurance control and stochastic differential games
AbstractWe study stochastic differential games between two insurance companies who employ reinsurance to reduce risk exposure. We consider competition between two companies and construct a single payoff function of two companies' surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize the payoff function while its opponent is simultaneously choosing a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of the game and prove a verification theorem for a general payoff function. For the payoff function being the probability that the difference between two surplus reaches an upper bound before it reaches a lower bound, the game is solved explicitly.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 48 (2011)
Issue (Month): 1 (January)
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Web page: http://www.elsevier.com/locate/inca/505554
Non-proportional reinsurance HJB equation Ruin probability Stochastic control Stochastic differential game;
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- Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1998.
"Stochastic cooperative games in insurance and reinsurance,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-77120, Tilburg University.
- Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1996. "Stochastic Cooperative Games in Insurance and Reinsurance," Discussion Paper 1996-53, Tilburg University, Center for Economic Research.
- Hipp, Christian & Taksar, Michael, 2010. "Optimal non-proportional reinsurance control," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 246-254, October.
- Zeng, Xudong, 2010. "Optimal reinsurance with a rescuing procedure," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 397-405, April.
- Luo, Shangzhen & Taksar, Michael, 2012. "Minimal cost of a Brownian risk without ruin," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 685-693.
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