The Hedging Strategies Of Optimization In Insurance

In this paper, the background knowledge of hedging theory is given firstly, such as the basic principle, the basic method and the mathematical expression of hedging theory. Then the knowledge of stochastical analyse is considered, such as the thoery of martingale and Brown Motion, etc. And then we discuss the basic knowledge and theory on the financial market by mathematical symbol and formula, such as Discrete- time models, Black-Scholes models and European contingent claim can be priced well by martingale method. At last we discuss the insurance companies with payment process At hedge their risk to the level of minimax by buying stocks St, exchanging foreign- currency Qt and buying risk - free asset Bt in the financial market ( St, Qt, Bt ).The main job of this paper is enumerated as follows:1. The investment mode is extended: let the insurance company buy stocks St,exchange foreign-currency Qt, by risk-free asset Bt in the same time.2. The payment processes At are embodied, and gives out the basic fund process in the form of mathematics.3. Aplly the United-Linked Insurace Contracts with Guarantee to give out the basic payment mode. In virtue of Galtchouk-Kunita-Watanabe Decomposition Theorem to decomposite the natural value prcess V_t~* to update the risk expression, then we can get the hedging strategies of optimization with minimal risk.4. A realistic example is given out to apply the important conclusion in this paper. The text is organized as follows:Chapter 1 is introduction: introduces some substance and mathematical expression of hedging theory.Chapter 2 is the relative theory of stochastical analyse: including martingale, Brown Motion, Ito formula, Girsanov theorem, Markov process and Lipschitz condition etc.Chapter 3 is the relative theory of the financial market: the knowledge of discrete time model and Black-Scholes model, etc.Chapter 4 is the hedging strategies of optimization in insurance:In virtue of Galtchouk-Kunita-Watanabe Decomposition Theorem to decomposite the natural value prcess V_t~* toupdate the risk expression, then we can get the hedging strategies of optimization with minimal risk.