Open AccessOptimal per-loss reinsurance and investment to minimize the probability of drawdown
Author(s) -
Xia Han,
Zhibin Liang,
Yu Yuan,
Caibin Zhang
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021145
Subject(s) - reinsurance , drawdown (hydrology) , investment (military) , value (mathematics) , asset (computer security) , actuarial science , economics , mathematics , statistics , computer science , engineering , geotechnical engineering , computer security , politics , political science , law , aquifer , groundwater
In this paper, we study an optimal reinsurance-investment problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. We assume that the insurer can purchase per-loss reinsurance for each line of business and invest its surplus in a financial market consisting of a risk-free asset and a risky asset. Under the criterion of minimizing the probability of drawdown, the closed-form expressions for the optimal reinsurance-investment strategy and the corresponding value function are obtained. We show that the optimal reinsurance strategy is in the form of pure excess-of-loss reinsurance strategy under the expected value principle, and under the variance premium principle, the optimal reinsurance strategy is in the form of pure quota-share reinsurance. Furthermore, we extend our model to the case where the insurance company involves \begin{document}$ n $\end{document}\begin{document}$ (n\geq3) $\end{document} dependent classes of insurance business and the optimal results are derived explicitly as well.