| In addition to changing the current status of Chinese stock market, which is the investor can only get profit form the increase of stock price, the stock index future not only provide a hedge opportunity, but also give investor another profit model ,that is arbitrage. The principle is making use of the unreasonable price in stock index market. The investor take part in the transaction in the spot and future market, or different types of stock index contracts, or different periods of trading stock index contracts at the same time, in order to earn spreads. This profit model induces the development of index tracking.Optimization of index tracking can be summarized as a nonlinear mixed integer optimization problem, which is a much complex process. What's more, when establishing the objective function, few scholars take the background risk into account, in particular prudent investor preference, which relates to the third moment for the most value. We use linear method to overcome the problem of getting the maximum value of the third order moment. Based on the background risk under the framework of utility function, we establish index tracking model. There are two kinks of investors, risk aversion and prudent. Based on the investor types we induce constrain conditions and objective functions to establish mathematic model. We choose HS300 as the first tracking target and the SZ100 as the second tracking target, which provide some comparisons. Based on different models we carry out the calculation and compare the tracking result. The result shows if we only care the tracking deviation, the three-period models which is for risk aversion investors, is the best. The tracked index using the model for prudent investors gets a positive deviation, just as we anticipant. We simplify the index tracking problem using linear method in this paper. At the same time the calculate speed is well developed and the result is as we anticipant, which provide convenient for the use of index tracking in practice. |
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