Chinese Journal of Management Science ›› 2023, Vol. 31 ›› Issue (12): 11-22.doi: 10.16381/j.cnki.issn1003-207x.2022.2771
Previous Articles Next Articles
Received:
2022-07-15
Revised:
2023-03-01
Online:
2023-12-15
Published:
2023-12-20
Contact:
Zhi-dong LIU
E-mail:liu_phd@163.com
CLC Number:
Zhi-dong LIU,Chao WANG. Multi-Level Order Flow Imbalance and Price Impact[J]. Chinese Journal of Management Science, 2023, 31(12): 11-22.
"
所属行业 | 股票名称 | 日均市值(亿元) | 平均每日委托笔数 | 平均每日成交笔数 | 平均成交价格 | 平均买卖价差/ticks | 平均相对买卖价差 |
---|---|---|---|---|---|---|---|
房地产业 | 万科A | 3136.65 | 67545.76 | 46478.55 | 28.20 | 1.43 | 0.0005 |
招商蛇口 | 1607.33 | 23942.98 | 16592.60 | 20.60 | 1.67 | 0.0008 | |
荣安地产 | 90.19 | 10706.05 | 6376.27 | 2.97 | 1.05 | 0.0036 | |
南山控股 | 86.67 | 6038.54 | 3938.65 | 3.38 | 1.06 | 0.0032 | |
奥园美谷 | 42.24 | 8205.79 | 5180.85 | 6.01 | 1.16 | 0.0020 | |
国创高新 | 41.85 | 8146.80 | 5422.07 | 4.98 | 1.11 | 0.0023 | |
制造业 | 五粮液 | 4201.14 | 120095.98 | 75441.94 | 109.43 | 3.09 | 0.0003 |
宁德时代 | 1714.83 | 36375.01 | 23006.11 | 79.33 | 3.40 | 0.0004 | |
美利云 | 59.81 | 15673.36 | 10402.01 | 10.02 | 1.72 | 0.0017 | |
方大集团 | 59.91 | 13166.69 | 8516.81 | 6.07 | 1.10 | 0.0019 | |
宇晶股份 | 32.15 | 13813.38 | 8545.45 | 35.58 | 3.95 | 0.0011 | |
扬帆新材 | 32.11 | 8128.30 | 5196.50 | 19.52 | 2.19 | 0.0012 | |
信息传输、软件和信息技术服务业 | 科大讯飞 | 700.17 | 74298.34 | 49191.88 | 33.31 | 1.60 | 0.0005 |
巨人网络 | 384.87 | 13095.36 | 8516.66 | 19.83 | 1.63 | 0.0008 | |
恺英网络 | 72.99 | 26122.73 | 17087.23 | 3.58 | 1.06 | 0.0031 | |
海峡创新 | 72.27 | 9656.60 | 6372.36 | 10.77 | 1.51 | 0.0014 | |
汇纳科技 | 37.39 | 6413.50 | 3292.53 | 38.18 | 7.08 | 0.0019 | |
高伟达 | 36.76 | 18999.89 | 12760.92 | 8.84 | 1.30 | 0.0015 | |
金融业 | 平安银行 | 2483.71 | 70165.24 | 47669.19 | 14.03 | 1.15 | 0.0008 |
宁波银行 | 1251.79 | 28943.84 | 20307.12 | 23.50 | 1.68 | 0.0007 | |
长城证券 | 424.33 | 50612.67 | 34384.10 | 14.11 | 1.36 | 0.0010 | |
西部证券 | 336.20 | 32075.42 | 21238.76 | 10.28 | 1.17 | 0.0011 | |
东北证券 | 200.90 | 27801.23 | 19593.62 | 8.98 | 1.16 | 0.0013 | |
张家港行 | 107.62 | 19750.81 | 12622.06 | 6.29 | 1.07 | 0.0017 | |
农、林、牧、渔业 | 温氏股份 | 1958.87 | 45723.77 | 31224.76 | 37.63 | 2.37 | 0.0006 |
牧原股份 | 1415.20 | 45698.69 | 29762.98 | 71.11 | 4.20 | 0.0006 | |
仙坛股份 | 74.20 | 25230.67 | 17032.47 | 20.15 | 1.73 | 0.0009 | |
登海种业 | 69.38 | 27499.02 | 18241.67 | 8.94 | 1.37 | 0.0015 | |
众兴菌业 | 27.94 | 7013.10 | 4617.45 | 8.04 | 1.21 | 0.0015 | |
百洋股份 | 27.00 | 9428.61 | 6311.98 | 7.01 | 1.27 | 0.0018 |
"
股票名称 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
万科A | 0.01 | 10.05 | 2.98 | 8.32 | 1.86 | 3.66 | 5.46 | 1.41 | 2.57 | 2.89 | 3.88 |
招商蛇口 | 0.00 | 12.79 | 4.83 | 10.00 | 3.07 | 4.92 | 6.60 | 2.27 | 3.60 | 3.74 | 4.79 |
荣安地产 | -0.01 | 69.49 | 4.03 | 45.17 | 1.78 | 15.77 | 29.47 | 0.90 | 8.85 | 20.67 | 18.68 |
南山控股 | 0.00 | 79.12 | 5.71 | 44.22 | 1.28 | 16.68 | 28.92 | 0.48 | 12.45 | 16.57 | 15.72 |
奥园美谷 | 0.01 | 36.36 | 4.72 | 27.94 | 2.03 | 10.44 | 18.81 | 1.36 | 6.40 | 10.50 | 12.91 |
国创高新 | 0.00 | 37.56 | 5.03 | 29.78 | 2.44 | 11.02 | 19.20 | 1.50 | 5.88 | 9.03 | 16.25 |
五粮液 | 0.01 | 1.73 | 0.84 | 1.25 | 0.65 | 0.60 | 1.04 | 0.55 | 0.48 | 0.55 | 0.82 |
宁德时代 | 0.01 | 3.13 | 1.73 | 2.09 | 1.36 | 1.10 | 1.69 | 1.17 | 0.87 | 0.99 | 1.31 |
美利云 | 0.01 | 17.40 | 5.24 | 13.83 | 3.26 | 6.86 | 8.81 | 2.26 | 4.82 | 5.49 | 6.08 |
方大集团 | 0.01 | 39.72 | 4.17 | 29.72 | 1.52 | 11.73 | 17.66 | 1.02 | 7.16 | 8.76 | 14.67 |
宇晶股份 | 0.01 | 6.10 | 3.19 | 4.24 | 2.31 | 2.47 | 3.10 | 1.87 | 1.88 | 1.97 | 2.38 |
扬帆新材 | 0.01 | 11.57 | 4.30 | 9.59 | 2.93 | 5.14 | 6.42 | 2.25 | 3.65 | 4.03 | 4.71 |
科大讯飞 | 0.01 | 5.31 | 1.97 | 4.09 | 1.31 | 1.96 | 2.89 | 1.05 | 1.41 | 1.59 | 2.14 |
巨人网络 | 0.01 | 14.92 | 5.02 | 12.05 | 3.00 | 6.01 | 7.54 | 2.24 | 4.45 | 4.63 | 5.05 |
恺英网络 | 0.00 | 40.57 | 2.78 | 31.42 | 1.20 | 11.31 | 20.10 | 0.71 | 7.00 | 11.00 | 14.33 |
海峡创新 | 0.01 | 17.16 | 4.55 | 14.62 | 2.46 | 6.54 | 9.54 | 1.70 | 4.33 | 1.43 | 8.10 |
汇纳科技 | 0.00 | 8.74 | 4.99 | 5.49 | 3.80 | 3.41 | 3.91 | 3.20 | 2.71 | 2.74 | 2.78 |
高伟达 | 0.01 | 17.94 | 4.16 | 14.92 | 2.30 | 6.60 | 9.47 | 1.54 | 4.37 | 5.27 | 6.76 |
平安银行 | 0.00 | 20.66 | 4.53 | 17.47 | 2.47 | 6.75 | 10.70 | 1.70 | 4.46 | 5.15 | 7.44 |
宁波银行 | 0.00 | 10.02 | 4.02 | 7.84 | 2.73 | 3.86 | 5.44 | 2.17 | 2.79 | 3.13 | 3.88 |
长城证券 | 0.01 | 10.76 | 2.42 | 9.23 | 1.47 | 3.92 | 5.90 | 1.04 | 2.64 | 3.18 | 4.14 |
西部证券 | 0.00 | 26.67 | 3.89 | 22.63 | 1.86 | 8.53 | 13.70 | 1.27 | 5.28 | 7.55 | 8.82 |
东北证券 | 0.00 | 25.13 | 3.93 | 20.91 | 1.97 | 7.52 | 12.74 | 1.32 | 4.87 | 6.01 | 9.15 |
张家港行 | 0.00 | 40.37 | 3.74 | 31.73 | 1.68 | 11.07 | 19.35 | 1.02 | 6.20 | 10.04 | 13.98 |
温氏股份 | 0.00 | 5.39 | 2.52 | 3.72 | 1.82 | 1.84 | 2.64 | 1.49 | 1.42 | 1.49 | 1.96 |
牧原股份 | 0.01 | 2.49 | 1.39 | 1.54 | 1.14 | 0.78 | 1.24 | 1.00 | 0.63 | 0.70 | 0.99 |
仙坛股份 | 0.01 | 10.00 | 3.41 | 7.69 | 2.17 | 3.70 | 5.05 | 1.68 | 2.61 | 2.92 | 3.59 |
登海种业 | 0.01 | 17.28 | 4.15 | 14.49 | 2.26 | 6.53 | 9.27 | 1.55 | 4.20 | 5.06 | 7.12 |
众兴菌业 | 0.01 | 28.93 | 5.82 | 23.76 | 2.74 | 9.98 | 15.07 | 1.63 | 6.26 | 7.36 | 12.66 |
百洋股份 | 0.01 | 23.16 | 5.14 | 18.11 | 2.59 | 7.87 | 12.09 | 1.78 | 5.07 | 6.89 | 8.67 |
"
股票名称 | OPI[ | OPI[ | OPI[ | OPI[ | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
α | β | β | β | β | β | β | β | β | β | β | |
万科A | 0.13 | 99 | 67 | 100 | 53 | 85 | 99 | 47 | 76 | 84 | 96 |
招商蛇口 | 0.80 | 98 | 73 | 100 | 61 | 87 | 98 | 54 | 78 | 82 | 93 |
荣安地产 | 0.57 | 83 | 40 | 100 | 34 | 87 | 96 | 32 | 76 | 84 | 87 |
南山控股 | 1.14 | 82 | 45 | 100 | 37 | 84 | 93 | 34 | 73 | 81 | 86 |
奥园美谷 | 0.72 | 90 | 53 | 100 | 44 | 87 | 96 | 40 | 78 | 83 | 88 |
国创高新 | 1.07 | 92 | 57 | 100 | 47 | 89 | 96 | 43 | 79 | 84 | 88 |
五粮液 | 2.62 | 100 | 80 | 99 | 68 | 65 | 98 | 61 | 55 | 62 | 93 |
宁德时代 | 1.90 | 100 | 83 | 98 | 72 | 69 | 95 | 64 | 58 | 66 | 89 |
美利云 | 0.70 | 99 | 73 | 100 | 61 | 88 | 97 | 56 | 80 | 87 | 91 |
方大集团 | 0.63 | 91 | 49 | 100 | 40 | 89 | 96 | 36 | 79 | 84 | 90 |
宇晶股份 | 1.40 | 99 | 86 | 98 | 74 | 79 | 94 | 67 | 68 | 73 | 86 |
扬帆新材 | 1.23 | 98 | 77 | 99 | 66 | 85 | 95 | 61 | 77 | 79 | 88 |
科大讯飞 | 0.47 | 100 | 73 | 100 | 59 | 84 | 99 | 53 | 71 | 82 | 97 |
巨人网络 | 1.44 | 98 | 72 | 100 | 62 | 88 | 97 | 55 | 80 | 84 | 91 |
恺英网络 | 0.33 | 89 | 40 | 100 | 35 | 88 | 96 | 30 | 80 | 87 | 89 |
海峡创新 | 1.32 | 98 | 66 | 99 | 56 | 85 | 97 | 50 | 78 | 84 | 92 |
汇纳科技 | 2.09 | 98 | 79 | 94 | 71 | 75 | 84 | 66 | 67 | 67 | 74 |
高伟达 | 0.61 | 98 | 64 | 100 | 51 | 90 | 98 | 45 | 83 | 86 | 93 |
平安银行 | 0.17 | 99 | 57 | 100 | 46 | 87 | 99 | 40 | 79 | 84 | 96 |
宁波银行 | 0.68 | 99 | 73 | 100 | 61 | 88 | 98 | 55 | 77 | 83 | 94 |
长城证券 | 0.34 | 99 | 65 | 100 | 53 | 87 | 99 | 45 | 77 | 86 | 96 |
西部证券 | 0.39 | 96 | 53 | 100 | 44 | 89 | 98 | 40 | 80 | 86 | 93 |
东北证券 | 0.34 | 96 | 55 | 100 | 45 | 86 | 98 | 41 | 79 | 86 | 94 |
张家港行 | 0.09 | 91 | 46 | 100 | 38 | 88 | 96 | 35 | 80 | 86 | 90 |
温氏股份 | 0.55 | 100 | 78 | 99 | 66 | 72 | 98 | 59 | 62 | 72 | 93 |
牧原股份 | 1.36 | 100 | 86 | 97 | 77 | 59 | 94 | 72 | 49 | 58 | 88 |
仙坛股份 | 0.77 | 99 | 77 | 100 | 64 | 87 | 99 | 56 | 79 | 84 | 95 |
登海种业 | 0.48 | 97 | 64 | 100 | 52 | 90 | 98 | 47 | 82 | 87 | 94 |
众兴菌业 | 1.03 | 94 | 61 | 100 | 53 | 89 | 96 | 44 | 79 | 84 | 92 |
百洋股份 | 0.75 | 95 | 61 | 100 | 51 | 90 | 97 | 45 | 83 | 86 | 91 |
"
样本类型 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
样本内 | 0.25分位 | 0.138 | 0.451 | 0.567 | 0.634 | 0.677 | 0.707 | 0.732 | 0.749 | 0.764 | 0.775 |
中位数 | 0.222 | 0.629 | 0.767 | 0.829 | 0.864 | 0.885 | 0.901 | 0.913 | 0.922 | 0.929 | |
0.75分位 | 0.308 | 0.832 | 0.930 | 0.961 | 0.975 | 0.983 | 0.988 | 0.991 | 0.993 | 0.994 | |
中位数增幅(%) | - | 183.2 | 21.9 | 8.1 | 4.2 | 2.5 | 1.8 | 1.3 | 1.0 | 0.8 | |
P值 | - | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
样本外 | 0.25分位 | 0.043 | 0.275 | 0.360 | 0.405 | 0.429 | 0.436 | 0.431 | 0.417 | 0.396 | 0.362 |
中位数 | 0.149 | 0.458 | 0.571 | 0.625 | 0.652 | 0.663 | 0.666 | 0.662 | 0.654 | 0.642 | |
0.75分位 | 0.239 | 0.670 | 0.778 | 0.817 | 0.837 | 0.842 | 0.844 | 0.842 | 0.839 | 0.833 | |
中位数增幅(%) | - | 206.5 | 24.6 | 9.4 | 4.4 | 1.6 | 0.5 | -0.6 | -1.2 | -1.8 | |
P值 | - | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.97 | 0.00 |
1 | 邴涛,刘善存,张强,等. 指令驱动市场中非知情交易者的最优交易策略[J]. 管理科学学报, 2017, 20(3): 24-45. |
Bing Tao, Liu Shancun, Zhang Qiang, et al. The optimal trading strategy of uninformed traders in an order driven market[J]. Journal of Management Sciences in China, 2017, 20(3): 24-45. | |
2 | 郭梁, 周炜星. 基于高频数据的中国股市量价关系研究[J]. 管理学报, 2010, 7(8): 1242-1247. |
Guo Liang, Zhou Weixing. An empirical analysis of the volume-price relation using high-frequency data in the chinese stock market[J]. Chinese Journal of Management, 2010, 7(8): 1242-1247. | |
3 | Gould M D, Porter M A, Williams S, et al. Limit order books[J]. Quantitative Finance, 2013, 13(11): 1709-42. |
4 | O'Hara M. High frequency market microstructure[J]. Journal of Financial Economics, 2015, 116(2): 257-270. |
5 | Bouchaud J P, Bonart J, Donier J, et al. Trades, quotes and prices: financial markets under the microscope[M]. Cambridge University Press, 2018. |
6 | Capponi F, Cont R. Multi-asset market impact and order flow commonality[R]. Working Paper, Imperial College London,2020. |
7 | 谢文杰, 李牧遥, 周炜星. 噪声交易者、交易行为多样性与即时价格冲击[J]. 管理科学学报, 2020, 23(4): 98-109. |
Xie Wenjie, Li Muyao, Zhou Weixing. Noise traders,diversity of trading behavior,and immediate price impact of a stock and its warrant[J]. Journal of Management Sciences in China, 2020, 23(4): 98-109. | |
8 | Cont R. Statistical modeling of high-frequency financial data[J]. IEEE Signal Processing Magazine, 2011, 28(5): 16-25. |
9 | Hautsch N, Huang R. The market impact of a limit order[J]. Journal of Economic Dynamics and Control, 2012, 36(4): 501-522. |
10 | 刘志东, 赵致远, 王超. 指令流不平衡、指令爆发与价格冲击[J]. 系统工程理论与实践, 2022, 42(9): 2367-2390. |
Liu Zhidong, Zhao Zhiyuan, Wang Chao. Order flow imbalance, quote burst and price impact[J]. Systems engineering-Theory & Practice, 2022, 42(9): 2367-2390. | |
11 | 龚玉婷, 徐信喆, 杨朝军. 证券市场指令流与收益的非线性依赖性研究:混合连接函数(Mixed Copula)在流动性及流动性黑洞问题上的应用[J]. 管理工程学报, 2016, 30(3): 151-160. |
Gong Yuting, Xu Xinzhe, Yang Chaojun. Nonlinear dependence of order flow and return on stock market: applying mixed copula in the problem of liquidity and liquidity black hole[J]. Journal of Industrial Engineering/Engineering Management,2016, 30(3): 151-160. | |
12 | Eisler Z, Bouchaud J P, Kockelkoren J. The price impact of order book events: market orders, limit orders and cancellations[J]. Quantitative Finance, 2012, 12(9): 1395-419. |
13 | Bouchaud J P, Gefen Y, Potters M, et al. Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes[J]. Quantitative finance, 2004, 4(2): 176-90. |
14 | 陈收, 李双飞, 黎传国. 订单差、交易量变化对股票价格的冲击[J]. 管理科学学报, 2010, 13(9): 68-75+97. |
Chen Shou, Li Shuangfei, Li Chuanguo. Stock price response to order imbalance and change of volume[J]. Journal of Management Sciences in China, 2010,13(9): 68-75+97. | |
15 | Frazzini A, Israel R, Moskowitz T J. Trading costs of asset pricing anomalies[R]. Working Paper,AQR Capital Management, 2012. |
16 | Cont R, Kukanov A, Stoikov S. The price impact of order book events[J]. Journal of financial econometrics, 2014, 12(1): 47-88. |
17 | Xu Ke, Gould M D, Howison S D. Multi-level order-flow imbalance in a limit order book[J]. Market Microstructure and Liquidity, 2018, 4(03n04): 1950011. |
18 | Chan K, Fong W M. Trade size, order imbalance, and the volatility-volume relation[J]. Journal of Financial Economics, 2000, 57(2): 247-273. |
19 | Bouchaud J P. Price impact[R]. Working Paper, Capital Fund Management, 2009. |
20 | Wang Shanshan, Schäfer R, Guhr T. Cross-response in correlated financial markets: individual stocks[J]. The European Physical Journal B, 2016, 89(4): 1-16. |
21 | Brown P, Walsh D, Yuen A. The interaction between order imbalance and stock price[J]. Pacific-Basin Finance Journal, 1997, 5(5): 539-557. |
22 | Kyle A S. Continuous auctions and insider trading[J]. Econometrica: Journal of the Econometric Society, 1985: 1315-1335. |
23 | Andrade S C, Chang C, Seasholes M S. Trading imbalances, predictable reversals, and cross-stock price pressure[J]. Journal of Financial Economics, 2008, 88(2): 406-423. |
24 | Benzaquen M, Mastromatteo I, Eisler Z, et al. Dissecting cross-impact on stock markets: an empirical analysis[J]. Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017(2): 023406. |
25 | Pasquariello P, Vega C. Strategic cross-trading in the US stock market[J]. Review of Finance, 2015, 19(1): 229-282. |
26 | Cont R, Cucuringu M, Zhang Chao. Price impact of order flow imbalance: multi-level, cross-sectional and forecasting[J]. arXiv preprint arXiv: , 2021. |
27 | Ahn H J, Bae K H, Chan K. Limit orders, depth, and volatility: evidence from the stock exchange of Hong Kong[J]. The Journal of finance, 2001, 56(2): 767-788. |
28 | 赵秀娟, 魏卓,汪寿阳.基于日内效应的沪深300股指期货套利的分析[J].管理科学学报, 2015,18(1):73-86. |
Zhao Xiujuan, Wei Zhuo, Wang Shouyang. Study on CS1300 index futures' arbitrage based on intraday effect[J]. Journal of Management Sciences in China, 2015, 18(1): 73-86. | |
29 | 刘志东, 赵致远. 基于状态依赖Hawkes过程的我国股市限价指令簿事件激励效应研究[J]. 中国管理科学, 2022, 30(2): 1-13. |
Liu Zhidong, Zhao Zhiyuan. Research on excitation effect among limit order book events in chinese stock market based on state-dependent hawkes processes[J]. Chinese Journal of Management Science, 2022, 30(2): 1-13. | |
30 | Harris L E, Panchapagesan V. The information content of the limit order book: evidence from NYSE specialist trading decisions[J]. Journal of Financial Markets, 2005, 8(1): 25-67. |
31 | Madhavan A, Richardson M, Roomans M. Why do security prices change? A transaction-level analysis of NYSE stocks[J]. The Review of Financial Studies, 1997, 10(4): 1035-1064. |
32 | Giot P. Market risk models for intraday data[J]. The European Journal of Finance, 2005, 11(4): 309-324. |
33 | Hecq A, Margaritella L, Smeekes S. Granger causality testing in high-dimensional VARs: a post-double-selection procedure[J]. Journal of Financial Econometrics, 2023,21(3):915-958. |
34 | Brunnermeier M K. Information leakage and market efficiency[J]. The Review of Financial Studies, 2005, 18(2): 417-457. |
35 | Schneider M, Lillo F. Cross-impact and no-dynamic-arbitrage[J]. Quantitative Finance, 2019, 19(1): 137-154. |
36 | Harford J, Kaul A. Correlated order flow: pervasiveness, sources, and pricing effects[J]. Journal of Financial and Quantitative Analysis, 2005, 40(1): 29-55. |
[1] | LIU Zhi-dong, ZHAO Zhi-yuan. Research on Excitation Effect among Limit Order Book Events in Chinese Stock Market Based on State-dependent Hawkes Processes [J]. Chinese Journal of Management Science, 2022, 30(2): 1-13. |
[2] | XU Qi-fa, CAI Chao, JIANG Cui-xia. An Analysis of the Relationship between Order Imbalance and Stock Returns through Quantile Regression Approach for Large-scale Data [J]. Chinese Journal of Management Science, 2016, 24(12): 20-29. |
[3] | WANG Wen-hu, WAN Di-fang, WU Zu-guang, ZHANG Lu. Investors Structure、Order Imbalance and Price Discovery:Evidence from Shanghai Commodity Futures Market [J]. Chinese Journal of Management Science, 2015, 23(11): 1-11. |
[4] | CHEN Xiao-hong, HU Wei, WANG Zhi-yun. Empirical Research on Price Impact Factors of Carbon Exchange of Voluntary Market:Evidence from CCX of USA [J]. Chinese Journal of Management Science, 2013, 21(4): 74-81. |
[5] | ZHANG Qiang, LIU Shan-cun, LIN Qian-hui, QIU Wan-hua. The Effects of the Optimal Trading Strategies on Trading Durations [J]. Chinese Journal of Management Science, 2012, 20(5): 24-30. |
Viewed | ||||||
Full text |
|
|||||
Abstract |
|
|||||
|