股票交易最优数学模型.doc

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1、股票投资问题摘要本文通过对一支股票进行投资交易进行了分析研究，以求使亏损率与成本最优化。为此，我们摘用了一些网上股市数据我们以Excel与SAS对相关数据进行了分析，得出这一支股票的最佳投资方案。模型的假设：1）亏损率与交易次数有关，不受其他因素影响，为1/Xn；2）该股市所提供的数据都真实可靠；3）投资者原本所拥有的投资基金为1500000符号说明时间段——以半小时为一个时间段，9：30~10:00为1阶段，以此类推交易额——一个时间段的交易钱数数据的分析：摘用股市某股票某一天的数据，见附录。买入时间段交易额平均股价交易股数12328009.8623610.5522223429.822

2、687.9632531979.7425995.5945134259.7852497.445510009.85204.0826616539.796297.54971334319.7413699.2886369889.666352.92卖出时间段交易额平均股价交易股数14307469.85643703.9422790969.7928508.2736147069.7463111.543337589.5934802.715332399.793395.62185729.7822348.8876074419.7462365.61819248519.61200296.73.模型的建立：从以上买入与卖出

3、两个数据表，我们可以基本判断出在哪个时间段利于交易，从而可以得出以下几个投资方案：方案一：买入交易次数时间段金额（元）股数手续费（元）1863698866352.9263.69882451342552497.4451.34253325319725995.5925.319741963909775.8629.639总和　1500000154621.8150卖出181485915154621.8303.2133盈利（元）-13631.7867可知交易次数n为5次，所以亏损率为1/10，总成本费为453.21元，盈利为-13631.7867元方案二：买入交易次数时间段平均股价金额股数手续费139

4、.7425319725995.5925.3197219.8623280023610.5523.28329.822234222687.9622.2342479.7413343113699.2813.3431569.79616536297.5496.1653659.8510005204.0825.1749.7851342552497.4451.3425889.6321523349.1673.2152总和　　1500000153341.6150卖出179.7460744162365.61123.1097239.7461470663111.5124.5821319.856274632.72786

5、4.5155.32778总和　　1496780153341.6303.0196盈利-3673.369369可知交易次数n为11次，所以亏损率为1/22，总成本费为453.02元，盈利为-3673.369369元根据上面两种投资方案，可见方案二更为可行。timepricevolumstate9:349.872B9:349.884B9:359.881S9:369.871S9:379.8720S9:389.8743S9:409.8448S9:419.8769B9:429.8923B9:429.895S9:439.950B9:439.8910S9:459.8783S9:489.871S9:499

6、.8730S9:509.8726S9:519.875B9:519.8672S9:529.8316S9:549.8324S9:549.837B9:559.8313S9:559.832S9:569.8339S9:579.8310B9:579.833B9:589.8317B10:009.833S10:009.8346B10:019.836B10:029.8220S10:029.822S10:039.836B10:039.824S10:039.8217S10:049.8111S10:059.8115S10:059.8117S10:079.812B10:089.812S10:099.816B10:

7、099.87S10:099.84S10:109.82B10:109.82B10:139.7920B10:149.867B10:159.815B10:169.820S10:179.797S10:179.7810S10:189.781S10:189.786S10:189.797B10:199.7821S10:199.7819B10:209.785B10:209.788B10:219.793B10:229.797B10:239.839B1