Robust optimal investment–reinsurance strategies for an insurer with multiple dependent risks

This paper considers a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who is uncertain about the model parameters. We assume that the surplus of the insurance company can be allocated to the financial market consisting of one ri...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2019-11, Vol.89, p.157-170
Main Authors: Sun, Jingyun, Yao, Haixiang, Kang, Zhilin
Format: Article
Language:English
Subjects:
Ambiguity
Ambiguity-averse insurer
Assets
Expected utility
Financial market
Insurance
Insurance claims
Insurance companies
Investment
Investments
Mathematical models
Multiple dependent risks
Optimal control
Optimization
Parameter uncertainty
Program verification (computers)
Reinsurance
Robust optimal control
Robustness (mathematics)
Square-root factor process
Stochastic processes
Suboptimal strategy
Uncertainty
Utility loss
Verification
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Summary:This paper considers a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who is uncertain about the model parameters. We assume that the surplus of the insurance company can be allocated to the financial market consisting of one risk-free asset and one risky asset whose price process satisfies square root factor process. Under the objective of maximizing the expected utility of the terminal surplus, by adopting the technique of stochastic control, closed-form expressions of the robust optimal strategy and the corresponding value function are derived. The verification theorem is also provided. Finally, by presenting some numerical examples, the impact of some parameters on the optimal strategy is illustrated and some economic explanations are also given. We find that the robust optimal reinsurance strategies under the generalized mean–variance premium are very different from that under the variance premium principle. In addition, ignoring model uncertainty risk will lead to significant utility loss for the AAI.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2019.09.006