股票交易最优数学模型

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，9：3010:00为1阶段，以此类推交易额一个时间段内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12328009.8623610.5522223429.822687.96

2、32531979.7425995.5945134259.7852497.445510009.85204.0826616539.796297.54971334319.7413699.2886369889.666352.92卖出时间段交易额平均股价交易股数14307469.85643703.9422790969.7928508.2736147069.7463111.543337589.5934802.715332399.793395.19962185729.7822348.8876074419.7462365.61819248519.61200296.73.模型的建立：从以上买入与卖出两个数据表，

3、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139.742531972

4、5995.5925.3197219.8623280023610.5523.28329.822234222687.9622.2342479.7413343113699.2813.3431569.79616536297.5496.1653659.8510005204.0825.1749.7851342552497.4451.3425889.6321523349.1673.2152总和1500000153341.6150卖出179.7460744162365.61123.1097239.7461470663111.5124.5821319.856274632.727864.5155.32778总和1

5、496780153341.6303.0196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。timepricevolumstate9:349.872B9:349.884B9:359.881S9:369.871S9:379.8720S9:389.8743S9:409.8448S9:419.8769B9:429.8923B9:429.895S9:439.950B9:439.8910S9:459.8783S9:489.871S9:499.8730S9:509.8726S9:5

6、19.875B9:519.8672S9:529.8316S9:549.8324S9:549.837B9:559.8313S9:559.832S9:569.8339S9:579.8310B9:579.833B9:589.8317B10:009.833S10:009.8346B10:019.836B10:029.8220S10:029.822S10:039.836B10:039.824S10:039.8217S10:049.8111S10:059.8115S10:059.8117S10:079.812B10:089.812S10:099.816B10:099.87S10:099.84S10:109

7、.82B10:109.82B10:139.7920B10:149.867B10:159.815B10:169.820S10:179.797S10:179.7810S10:189.781S10:189.786S10:189.797B10:199.7821S10:199.7819B10:209.785B10:209.788B10:219.793B10:229.797B10:239.839B10:249.791S10:259.7910S10:259.791S10:269.792S10:269.792S10:269.796S10:279.7877S10:289.783B10:299.782S10:30

8、9.778S10:309.7720B10:309.7612S10:319.7640S10:329.761S10:329.7621S10:329.7618B10:339.75130S10:339.755B10:339.7530B10:339.753B10:339.754B10:349.788B10:359.751S10:359.7365S10:379.752S10:389.7533S10:389.755B10:399.754B10:399.7330S10:399.738S10:409.7210S10:409.724B10:409.729B10:419.721S10:419.725B10:419.

9、7220B10:419.7212B10:419.722B10:429.723B10:429.7220B10:429.725B10:429.722B10:439.7214B10:439.7147S10:439.716B10:449.716B10:449.715S10:469.756B10:469.751B10:489.754B10:489.75169S10:499.755B10:519.7530B10:519.7210S10:529.7510B10:549.7510B10:549.7310S10:599.7331S10:599.735S11:009.741S11:009.749B11:009.7

10、411S11:019.7419B11:019.7382S11:019.7353B11:039.745B11:039.746B11:039.749B11:049.741S11:049.7533B11:059.7541S11:069.762B11:069.7515S11:089.741S11:089.742S11:089.741B11:099.7350S11:109.7323S11:119.732S11:119.755B11:129.754B11:129.756B11:139.7615B11:139.81202B11:149.8255B11:159.8211B11:209.8100S11:209.

11、8575B11:219.8510B11:259.853B11:259.8210S11:259.825S11:269.8510B11:309.779S11:309.781S13:059.841B13:079.831B13:079.8328B13:139.81S13:189.794S13:209.792B13:229.791S13:249.788S13:259.786B13:279.785B13:289.7720S13:309.779B13:319.7620S13:319.7719B13:329.772B13:349.773S13:349.776B13:379.827B13:399.822B13:

12、409.814B13:419.815S13:429.8110S13:439.75124S13:449.7543S13:459.819B13:479.811S13:509.83S13:549.785S13:559.785B13:569.777S13:569.772S13:579.771S13:589.772B13:589.777B14:019.779S14:019.7710S14:029.762S14:039.7521S14:059.753S14:059.7585S14:069.7515B14:069.741S14:079.7420S14:079.733S14:079.7351S14:099.7

13、310B14:109.7321B14:109.7210S14:109.7230S14:119.7220S14:129.742S14:139.742B14:149.7318S14:159.7310S14:159.7310S14:159.733S14:169.733S14:169.7476B14:189.7511B14:219.753S14:219.75112S14:229.7313S14:229.72148S14:249.7114S14:249.715S14:259.731B14:269.731B14:279.721S14:279.7217S14:319.721S14:319.726S14:31

14、9.7260S14:329.723S14:329.71181S14:339.721S14:339.7110S14:339.6920S14:349.683S14:349.688S14:349.675S14:349.6524S14:349.652S14:359.6530S14:359.6619B14:359.6510S14:359.6639B14:359.6542S14:359.6512S14:359.6626B14:359.6619S14:369.661S14:369.675B14:369.659S14:379.653B14:379.6510B14:379.6410S14:379.656B14:

15、379.6310S14:379.6117S14:389.613S14:389.67S14:389.611B14:389.611B14:389.611B14:389.614B14:399.632B14:409.638B14:419.6100S14:429.64S14:429.6212B14:439.636B14:439.6220S14:439.6413B14:439.6513B14:449.6520B14:449.654B14:449.6920B14:459.651S14:459.6363S14:459.635B14:469.632B14:479.6321B14:479.624S14:489.6

16、25B14:489.622S14:489.6130S14:499.633B14:499.61B14:499.610B14:499.68B14:499.594S14:499.63B14:499.63B14:509.63B14:509.62B14:509.610B14:509.5944S14:509.592B14:509.595B14:509.594B14:519.5767S14:519.572B14:519.5620S14:519.5610S14:519.5610S14:529.57141B14:529.573S14:529.559S14:529.5610B14:539.565B14:539.5510S14:539.552B14:549.542