Dynamic changes and multi-dimensional evolution of portfolio optimization

Figures & data

Figure 1. The number of published papers per year of portfolio optimization research.

Source: Web of Science.

Figure 2. The document types of portfolio optimization research.

Source: Web of Science.

Table 2. The top 10 research areas of portfolio optimization research.

Research areas	Number	The percentage
Business Economics	2013	34.91%
Mathematics	1665	28.87%
Operations Research Management Science	1639	28.42%
Engineering	1184	20.53%
Computer Science	1041	18.05%
Mathematical Methods in social sciences	499	8.65%
Energy fuels	353	6.12%
Environment Sciences Ecology	246	4.27%
Science Technology Other Topics	234	4.06%
Automation Control Systems	203	3.52%

Source: Web of Science.

Table 1. The top 10 WoS categories of portfolio optimization research.

WoS categories	Number	The percentage
Operations Research Management Science	1639	28.42%
Economics	975	16.91%
Business Finance	798	13.84%
Mathematics Interdisciplinary Applications	739	12.81%
Mathematics Applied	721	12.50%
Management	705	12.22%
Social Sciences Mathematical Methods	499	8.65%
Computer Science Artificial Intelligence	487	8.44%
Engineering Electrical Electronic	433	7.51%
Statistics Probability	404	7.01%

Source: Web of Science.

Figure 3. The author's collaboration of portfolio optimization research.

Source: Citespace.

Table 3. Top 20 productive authors of portfolio optimization research.

Authors	Year	Number	Authors	Year	Number
Li, D.	2008	27	Liu, Y. J.	2012	14
Zhang, W. G.	2007	26	Rustem, B.	2007	14
Chen, Z. P.	2007	25	Zenios, S.	1994	13
Mukensh, K. M.	2013	19	Yao, H. X.	2013	13
Fabozzi, F. J	2007	19	Li, X.	2014	12
Huang, X.X.	2007	18	Kim, J.H.	2013	12
Gupta, P.	2013	17	Konno, H.	1999	12
Kim, W. C.	2013	15	Wang, S. Y.	2008	11
Chen, W.	2011	15	Wong, H. Y.	2016	11
Knoke, T.	2013	15	Fernandez, E.	2015	11

Source: Citespace.

Figure 4. The institution collaboration of portfolio optimization research.

Source: Citespace.

Table 4. Top 10 productive institutions of portfolio optimization research.

Institutions	Countries	Number	Percentage
The Chinese University of Hong Kong	China	78	1.35%
Chinese Academy of Sciences	China	66	1.14%
University of Waterloo	Canada	59	1.02%
The Hong Kong Polytechnic University	China	57	0.99%
Sun Yat-sen University	China	55	0.95%
Xi’an Jiaotong University	China	51	0.88%
Massachusetts Institute of Technology	USA	49	0.85%
University London Imperial College of Sciences Technology & Medicine	England	46	0.80%
Columbia University	USA	41	0.71%
Imperial College London	UK	39	0.68%

Source: Citespace.

Table 5. Top 10 productive countries/territories of portfolio optimization research.

Countries/Territories	Number	Percentage
China	1357	23.53%
USA	1318	22.59%
England	521	9.03%
Germany	430	7.46%
Italy	299	5.18%
France	294	5.10%
Canada	294	5.10%
Australia	236	4.10%
Spain	213	3.69%
Iran	196	3.40%

Source: Citespace.

Figure 5. The country collaboration of portfolio optimization research.

Source: Citespace.

Figure 6. The cluster network of portfolio optimization research.

Source: Citespace.

Table 6. The largest 10 clusters of portfolio optimization research.

Cluster	Size	Silhouette	Label (LLR)	Mean
0	97	0.749	Robust optimization	2008
1	94	0.867	Stochastic control	1994
2	94	0.884	Stochastic optimization	1998
3	91	0.739	Cardinality constraints	2012
4	85	0.809	Data envelopment analysis	2015
5	84	0.85	Fuzzy portfolio selection	2006
6	79	0.815	Consumption and investment problems	2000
7	77	0.78	Stochastic dominance	2001
8	72	0.849	Dynamic programming	2008
9	34	0.887	Stochastic optimization	2001

Source: Citespace.

Table 7. Top 15 cited references for portfolio optimization research.

References	Source	Frequency
DeMiguel et al. (2009b)	The Review of Financial Studies	142
Kolm et al. (2014)	European Journal of Operational Research	100
DeMiguel et al. (2009a)	Management Science	93
Li et al. (2010)	European Journal of Operational Research	62
Rockafellar and Uryasev (2002)	Journal of Banking & Finance	59
Zhu and Fukushima (2009)	Operations Research	59
Björk et al. (2014)	Mathematical Finance	57
Rockafellar et al. (2007)	Journal of Banking & Finance	55
Artzner et al. (1999)	Mathematical Finance	52
Woodside-Oriakhi et al. (2011)	European Journal of Operational Research	51
Goldfarb and Iyengar (2003)	Mathematics of Operations Research	51
Anagnostopoulos and Mamanis (2011)	Expert Systems with Applications	49
Garlappi et al. (2007)	The Review of Financial Studies	49
Basak and Chabakauri (2012)	The Review of Financial Studies	47
Tu and Zhou (2011)	Journal of Financial economics	47

Source: Citespace.

Table 8. Top 20 cited references with the strongest citation burst.

References	Strength	Begin	End	1966–2021
Konno and Yamazaki (1991)	15.2711	1994	1999
Cariño et al. (1994)	10.0096	1995	2002
Cvitanic and Karatzas (1992)	5.8875	1997	2000
Zenios (1995)	5.8875	1997	2000
Golub et al. (1995)	8.381	1997	2003
Mulvey and Vladimirou (1992)	5.2324	1997	2000
Elton et al. (1996)	4.2126	1998	2003
Dantzig and Infanger (1993)	4.5164	1998	2001
Zenios and Kang (1993)	4.5562	1999	2001
Speranza (1993)	4.5562	1999	2001
Ogryczak and Ruszczyński (1999)	12.6376	1999	2007
Konno and Watanabe (1996)	4.7161	1999	2004
Cariño and Ziemba (1998)	6.8375	1999	2006
Bielecki and Pliska (1999)	7.3648	1999	2006
Cuoco (1997)	4.8518	2000	2004
Young (1998)	10.327	2000	2006
El Karoui and Jeanblanc-Picqué (1998)	5.4264	2000	2006
El Karoui and Quenez (1995)	5.2364	2000	2002
Karatzas and Shreve (2000)	15.2435	2000	2006
Kramkov and Schachermayer (1999)	9.5464	2000	2007

Source: Citespace.

Table 9. Top 12 keywords with the strongest citation bursts.

Keywords	Strength	Begin	End	1966–2021
optimization	4.7552	1990	1996
portfolio optimization	4.1683	1991	1996
consumption	8.5908	1995	2004
asset	4.8604	1997	2012
arbitrage	4.1961	2000	2007
contingent claim	4.3641	2000	2004
asset allocation	12.2987	2006	2014
approximation	5.6789	2008	2013
allocation	6.9677	2011	2017
algorithm	20.634	2012	2017
algorithm portfolio	5.2525	2013	2019
adaptation	8.5081	2015	2021

Source: Citespace.

Figure 7. The local forward main path of portfolio optimization research.

Source: Pajek.

Figure 8. The local backward main path of portfolio optimization research.

Source: Pajek.

Figure 9. The global standard main path of portfolio optimization research.

Source: Pajek.

Figure 10. The global key-route main path of portfolio optimization research.

Source: Pajek.

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