@article{Su2023, 
author = {Yiming Su and Haiyan Liu and Mi Chen},
title = {Robust equilibrium reinsurance and investment strategy for the insurer and reinsurer under weighted mean-variance criterion},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {10},
pages = {6384-6411},
keywords = {the insurer and reinsurer, loss-dependent premium principle, constant elasticity of variance model, weighted mean-variance criterion, ambiguity aversion},
url = {https://www.sciopen.com/article/10.3934/era.2023323},
doi = {10.3934/era.2023323},
abstract = {This paper investigates the time-consistent robust optimal reinsurance problem for the insurer and reinsurer under weighted objective criteria. The joint objective criterion is obtained by weighting the mean-variance objectives of both the insurer and reinsurer. Specifically, we assume that the net claim process is approximated by a diffusion model, and the insurer can purchase proportional reinsurance from the reinsurer. The insurer adopts the loss-dependent premium principle considering historical claims, while the reinsurance contract still uses the expected premium principle due to information asymmetry. Both the insurer and reinsurer can invest in risk-free assets and risky assets, where the risky asset price is described by the constant elasticity of variance model. Additionally, the ambiguity-averse insurer and ambiguity-averse reinsurer worry about the uncertainty of parameter estimation in the model, therefore, we obtain a robust optimization objective through the robust control method. By solving the corresponding extended Hamilton-Jacobi-Bellman equation, we derive the time-consistent robust equilibrium reinsurance and investment strategy and corresponding value function. Finally, we examined the impact of various parameters on the robust equilibrium strategy through numerical examples.}
}