Robust equilibrium investment-reinsurance strategy for n competitive insurers with square-root factor process

Abstract

We investigate a robust equilibrium investment-reinsurance problem for n ambiguity-averse competitive insurers, $n\ge 2$. Each insurer is allowed to purchase proportional reinsurance and invest in a risk-free asset and a risky asset. Each insurer aims to maximize the expected utility of a weighted relative terminal wealth with respect to the other competitors. In this article, the risky asset is assumed to follow a general and flexible model: the square root factor process. Following the game theory approach, we derive the closed solutions of the robust equilibrium investment-reinsurance strategies. Moreover, the verification theorem is provided in this article. Finally, we demonstrate some numerical analyses and give the economic explanations as well.

2020 Mathematics Subject Classification:

• 93E20
• 97M30

Keywords:

• Ambiguity-averse
• exponential utility
• relative performance concerns
• robust equilibrium strategy
• square-root factor process

Additional information

Funding

Support by the National Natural Science Foundation of China (No. 12071107) and State Scholarship Fund (No.201906705011).