Optimal Portfolio Selection Bounded By Safety-First Criterion For Insurer

The income of insurance companies comes from two main parts:the underwriting business and the investment business. With the development of China’s economy, the competitions of insurance companies become more fiercely. Relying on the traditional underwriting premiums has not been sufficient to meet the needs of its earnings, thus it has to turn to the investment business. Insurance investment business means the company will use the temporarily idle funds to invest for getting the benefits, which can increase the profits of the company, improve the competitiveness and also can further promote the development of capital market. With the gradual recovery of the economy and the opening up of the investment policy, the companies are faced with both opportunities and challenges. How to make the right decisions and improve the company’s profits has become an important issue faced by the insurer.The first criterion is suggested by Roy in 1952. He thought the investors have in mind some disaster level of returns and they behave so as to minimize the probability of disaster. Given that the insurance company’ management rely on debt, the security is the primary principles. While the first criterion focus on the security of assets, it is more suitable for the insurers.In this paper, we assume that the surplus of an insurer follows the compound Poisson risk process and the insurer would invest its surplus under continuous and discrete time frame-work, which consists of one-free bond and n risky assets. Given an acceptable disaster level, the safety-first criterion is chosen to establish a model, which is the optimal investment strategy for insurer. By Lagrange multiplier method and multi-layer optimization model, the explicit expression of optimal investment strategy and efficient frontier is derived. Then the optimal investment strategies and efficient frontier affected by the discounted value of the cumulative claims, claim risk and ruin probability are analyzed. Finally, by datum the investment procedure is simulated.