Abstract: This paper researches reinsurance-investment problem in incomplete markets.Under the assumptions that claim process of an insurance company follows diffusion process and the financial market is incomplete,by solving a quadratic optimization problem and a quadratic optimization dual problem with constraints,optimal constant rebalance strategies and corresponding effective frontier under mean-variance and mean-VaR models are obtained,respectively,for reinsurance-investment problem in Black-Scholes market with multiple risky assets.By comparing the results under mean-variance and mean- VaR models with each other,we find that the optimal const antrebalance strategies for two models are some multiples of a given commonfund,yet the optimal multiple for each model may not be identical; And the effective frontieres for two models are rays,yet the initial point and slope(risk price) of the rays may not be identical respectively.

Key words: Reinsurance-Investment, Mean-variance model, Mean-VaR model, constant rebalance strategy