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考虑到中国证券交易的限制规定及现实投资者并非完全理性的决策行为,给出了组合投资收益-损失风险双目标概率准则的整数规划模型。通过证券收益经验分布,应用分层抽样的随机模拟,并结合动态变化算子的遗传算法,构造GASS II遗传模拟混合算法,进行概率准则模型的优化求解。股票相关性由其秩相关系数给出,算法将秩和区间划分相联系,指导分层抽样。GASS II算法能有效刻画收益分布的“高峰厚尾”,激发遗传算法的隐含并行搜索特性,避免早熟现象,提高寻优效率与精度。最后给出了一个投资组合实证分析算例的收益-损失风险有效前沿。
Considering the restriction of securities trading in China and the fact that real investors are not completely rational decision-making, an integer programming model of portfolio investment return-loss probability of two-objective probability criterion is given. Based on the empirical distribution of securities returns, a stochastic simulation based on stratified sampling and a genetic algorithm based on dynamic change operator are used to construct a hybrid GASS II genetic algorithm to solve the probabilistic criterion model. The stock correlation is given by its rank correlation coefficient. The algorithm associates rank and interval divisions and directs stratified sampling. The GASS II algorithm can effectively characterize the “peak thick tail” of income distribution and stimulate the implicit parallel search characteristics of genetic algorithms to avoid premature phenomena and improve the efficiency and precision of optimization. Finally, we give a profit-loss risk effective frontier of an example of portfolio empirical analysis.