西安交通大学博士学位论文 4多期最坏情况风险度量及其在多阶段投资组合选择中的应用 4.1多期最坏情况风险度量的定义 42基于 w CVaR的多阶段鲁棒投资组合选择 4.3数值实验 44小结 5矩信息未知的可加型鲁棒风险度量及其在多期投资策略选择中的应用 5.1矩信息未知的单期鲁棒投资策略选择 52基于可加型风险度量的多期矩信息未知鲁棒投资策略选择…… 53实证研究 531数据集 532不确定集中参数的估计 533样本外表现 54小结 6矩信息未知的递归型鲁棒风险度量及其在多期投资组合选择中的应用 6.1新不确定集下的单期鲁棒投资组合选择模型 62基于递归型风险度量的多期矩信息未知鲁棒投资组合选择模型 63实证研究 64小结 7基于机制转换的多期鲁棒风险度量及其在多期投资问题中的应用 7.1多期最坏机制风险度量和多期混合最坏情况风险度量 72基于wr(VaR和 mw CVaR的多期鲁棒投资模型 7.3实证研究 74小结 8目标达成型风险度量及其在多期投资策略选择中的应用 599% 8.1概率目标首达时和新型动态风险度量 82目标达成型风险度量的性质 83目标达成型风险度量与VaR和方差的关系 8.4基于目标达成型风险度量的多期投资策略选择 106 84.1给定概率目标首达时的子问题 8.4.2辅助问题的解析解 110 843最优乘子… 844最优概率目标首达时 114 85实证研究 851在资本市场中的应用 8.52与动态MV模型的比较 116 8.6小结 …117 VIII‹SœåÆƨƆÿ© 4 ıœÅÄú¹ºx›˛9Ÿ3ı„›]|‹¿J•A^ ······························ 48 4.1 ıœÅÄú¹ºx›˛½¬ ··········································································· 48 4.2 ƒu wCVaR ı„°ï›]|‹¿J ························································ 50 4.3 Íä¢ ············································································································· 55 4.4 ( ····················································································································· 56 5 ›&Eôå\.°ïºx›˛9Ÿ3ıœ›]¸—¿J•A^ ··············· 57 5.1 ›&Eô¸œ°ï›]¸—¿J ······························································· 57 5.2 ƒuå\.ºx›˛ıœ›&Eô°ï›]¸—¿J ···························· 60 5.3 ¢yÔƒ ············································································································· 64 5.3.1 Í‚8 ·········································································································· 65 5.3.2 ÿ(½8•ÎÍO ··············································································· 65 5.3.3  Ly ··································································································· 66 5.4 ( ····················································································································· 67 6 ›&Eô48.°ïºx›˛9Ÿ3ıœ›]|‹¿J•A^ ··············· 69 6.1 #ÿ(½8e¸œ°ï›]|‹¿J. ··················································· 69 6.2 ƒu48.ºx›˛ıœ›&Eô°ï›]|‹¿J. ····················· 74 6.3 ¢yÔƒ ············································································································· 77 6.4 ( ····················································································································· 81 7 ƒuÅõ=Üıœ°ïºx›˛9Ÿ3ıœ›]ØK•A^ ······················ 82 7.1 ıœÅÄÅõºx›˛⁄ıœ·‹ÅÄú¹ºx›˛ ···································· 82 7.2 ƒu wrCVaR ⁄ mwCVaR ıœ°ï›]. ············································ 85 7.3 ¢yÔƒ ············································································································· 89 7.4 ( ····················································································································· 94 8 8Ià§.ºx›˛9Ÿ3ıœ›]¸—¿J•A^ ······································ 95 8.1 V«8Iƒàû⁄#.ƒºx›˛ ······························································· 95 8.2 8Ià§.ºx›˛5ü ·············································································· 97 8.3 8Ià§.ºx›˛Ü VaR ⁄ê'X ······················································ 102 8.4 ƒu8Ià§.ºx›˛ıœ›]¸—¿J ················································ 106 8.4.1 â½V«8IƒàûfØK ···································································· 107 8.4.2 9œØK)¤) ······················································································· 110 8.4.3 Å`¶f ······································································································ 113 8.4.4 Å`V«8Iƒàû ··················································································· 114 8.5 ¢yÔƒ ············································································································· 114 8.5.1 3]½|•A^ ··················································································· 114 8.5.2 ܃ MV .' ··············································································· 116 8.6 ( ····················································································································· 117 VIII