Time-consistent robust investment-reinsurance strategy with common shock dependence under CEV model

Area of Science:

• Quantitative Finance
• Risk Management
• Insurance Mathematics

Background:

• Insurers face complex risks from common shock dependent claims.
• Ambiguity aversion significantly impacts decision-making in insurance and investment.
• Dynamic financial markets, like those with Constant Elasticity of Variance (CEV) models, add layers of complexity.

Purpose of the Study:

• To derive the optimal robust equilibrium investment and reinsurance strategy for an ambiguity-averse insurer (AAI).
• To analyze the impact of ambiguity aversion and market dynamics on risk management decisions.
• To provide a framework for optimizing insurer wealth processes under uncertainty.

Main Methods:

• Utilizing a game theory framework with a mean-variance criterion.
• Applying stochastic control theory to solve the extended Hamilton-Jacobi-Bellman (HJB) equations.
• Developing a model for proportional reinsurance with premiums based on the expected value principle.

Main Results:

• The robust optimal investment-reinsurance strategy was derived.
• The equilibrium value function for the ambiguity-averse insurer was obtained.
• Numerical examples demonstrated the influence of various parameters on the optimal strategy.

Conclusions:

• The study successfully outlines a robust optimal strategy for investment and reinsurance under ambiguity.
• The findings highlight the importance of considering ambiguity aversion in insurer decision-making.
• The derived strategy offers practical implications for insurers managing dependent risks and market volatility.