This paper investigates the optimal mean-variance reinsurance-investment problem for an insurer with a common shock dependence under two kinds of popular premium principles: the variance premium principle and the expected value premium principle. We formulate the optimization problem within a game theoretic framework and derive the closed-form expressions of the equilibrium reinsurance-investment strategy and equilibrium value function under the two different premium principles by solving the extended Hamilton–Jacobi–Bellman system of equations. We find that under the variance premium principle, the proportional reinsurance is the optimal reinsurance strategy for the optimal reinsurance-investment problem with a common shock, while under the expected value premium principle, the excess-of-loss reinsurance is the optimal reinsurance strategy. In addition, we illustrate the equilibrium reinsurance-investment strategy by numerical examples and discuss the impacts of model parameters on the equilibrium strategy.
Keywords: Optimal reinsurance-investment, common shock, premium principles, mean-variance criterion, equilibrium strategy
@article{RO_2022__56_1_1_0,
author = {Bi, Junna and Li, Danping and Zhang, Nan},
title = {Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles},
journal = {RAIRO. Operations Research},
pages = {1--22},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {1},
doi = {10.1051/ro/2021183},
mrnumber = {4376289},
zbl = {1484.91374},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021183/}
}
TY - JOUR AU - Bi, Junna AU - Li, Danping AU - Zhang, Nan TI - Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles JO - RAIRO. Operations Research PY - 2022 SP - 1 EP - 22 VL - 56 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021183/ DO - 10.1051/ro/2021183 LA - en ID - RO_2022__56_1_1_0 ER -
%0 Journal Article %A Bi, Junna %A Li, Danping %A Zhang, Nan %T Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles %J RAIRO. Operations Research %D 2022 %P 1-22 %V 56 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021183/ %R 10.1051/ro/2021183 %G en %F RO_2022__56_1_1_0
Bi, Junna; Li, Danping; Zhang, Nan. Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles. RAIRO. Operations Research, Tome 56 (2022) no. 1, pp. 1-22. doi: 10.1051/ro/2021183
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