Abstract
This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.
Highlights
Risk management is a fundamental challenge for insurance companies
The surplus process is modelled by the jump-diffusion process
We investigate a mean-variance investment and reinsurance problem in a stochastic interest rate and stochastic volatility framework
Summary
Risk management is a fundamental challenge for insurance companies. Reinsurance is a powerful tool for insurers to transfer insurance risk. Browne (1995) [1] considered the problem of maximizing the expected utility and minimizing the ruin probability for insurers They derived the optimal investment strategies in a simple setting, where the surplus process is modelled by a drifted. We consider the time-consistent reinsurance and investment problem for mean-variance insurer incorporating both stochastic interest rate and stochastic volatility risk. The objective of insurer is to find an optimal reinsurance investment strategy in a time consistent sense, so as to maximize the expected value of terminal wealth and minimize the associated variance. The contribution of our paper is threefold: (1) we consider the time-consistent mean-variance optimization problem for insurers when considering both stochastic interest rate and stochastic volatility, which is new in the literature.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
