Equilibrium excess-of-loss reinsurance and investment strategies for an insurer and a reinsurer

Abstract

In this paper, we consider the equilibrium excess-of-loss reinsurance and investment problem for both an insurer and a reinsurer. The risk process of the insurer is described by a classical Cramér-Lundberg (C-L) risk model and the insurer can purchase excess-of-loss reinsurance from the reinsurer. Both the insurer and the reinsurer are allowed to invest in a financial market consisting of a risk-free asset and two risky assets. The market price of risk depends on a Markovian, affine-form and square-root stochastic factor process. Dynamic mean-variance criterion is considered in this paper. We aim to maximize the weighted sum of the insurer’s and the reinsurer’s objectives with different risk averse coefficients. By solving the corresponding extended Hamilton-Jacobi-Bellman (HJB) equations, we derive the equilibrium reinsurance and investment strategies and the corresponding equilibrium value function. Finally, the economic implications of our findings are illustrated.

Keywords:

• Reinsurance and investment
• insurer and reinsurer
• mean-variance criterion
• time-consistent strategy
• stochastic volatility

Additional information

Funding

This research was supported by National Natural Science Foundation of China (No. 11801179, 11871052, 11771329, 71771220, 11971172, 12071147, 71931004), the “Chenguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (No. 18CG26), the Fundamental Research Funds for the Central Universities (No. 2019ECNU-HWFW028), and the 111 Project, China (No. B14019).