Volume 56, Number 1, January-February 2022
|1 - 22
|07 February 2022
Equilibrium reinsurance-investment strategy with a common shock under two kinds of premium principles
School of Statistics, KLATASDS-MOE, East China Normal University, Shanghai, 200062, P.R. China
* Corresponding author: email@example.com
Accepted: 14 December 2021
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.
Mathematics Subject Classification: 90C39 / 91B30 / 91G80
Key words: Optimal reinsurance-investment / common shock / premium principles / mean-variance criterion / equilibrium strategy
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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