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Topic · Management Science and Operations Research

Risk and Portfolio Optimization

Risk and Portfolio Optimization is a research topic within Management Science and Operations Research. Science Explorer counts 12k research works in it since 1950. 10.2% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on robust optimization techniques for risk management and finance, including topics such as conditional value-at-risk, stochastic programming, portfolio optimization, uncertain data, coherent risk measures, and the Wasserstein metric. The papers explore methodologies and applications of robust optimization in addressing uncertainty and risk in financial decision-making.

  • Robust Optimization
  • Risk Management
  • Finance
  • Conditional Value-at-Risk
  • Stochastic Programming
  • Portfolio Optimization
  • Uncertain Data
  • Coherent Risk Measures
  • Wasserstein Metric
  • Convex Optimization
Research works
12k
fractional, since 1950
In the world top 10%
1.2k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+16%
the tick is no change
Largest producer
China
36% of the 10 largest, 2022-now
Risk and Portfolio Optimization

Which countries lead Risk and Portfolio Optimization research?

By volume, China and the United States publish the most (766 and 492 works in 2022-now).

By volume, 2022-now

  1. 1 China 766 works
  2. 2 United States 492 works
  3. 3 India 158 works
  4. 4 Germany 122 works
  5. 5 United Kingdom 119 works
  6. 6 France 118 works
  7. 7 Canada 117 works
  8. 8 Italy 115 works
  9. 9 Japan 62 works
  10. 10 Iran 62 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 35.9%United States: 23.1%India: 7.4%Germany: 5.7%6 others listed: 27.8%36%largest
China766 · 35.9%United States492 · 23.1%India158 · 7.4%Germany122 · 5.7%6 others listed593 · 27.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Risk and Portfolio Optimization research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Risk and Portfolio Optimization research, followed by Shandong University and University of Waterloo.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 36 works
  2. 2 Shandong UniversityChina 24 works
  3. 3 University of WaterlooCanada 21 works
  4. 4 Tsinghua UniversityChina 21 works
  5. 5 Georgia Institute of TechnologyUnited States 18 works
  6. 6 University of TorontoCanada 15 works
  7. 7 Hong Kong Polytechnic UniversityChina 14 works
  8. 8 Columbia UniversityUnited States 13 works
  9. 9 University of Science and Technology of ChinaChina 13 works
  10. 10 Chinese University of Hong KongChina 12 works

Who are the leading researchers in Risk and Portfolio Optimization?

The most-cited researchers publishing on Risk and Portfolio Optimization include Yoshua Bengio, Daniel J. Kahneman and Amos Tversky.

  1. 1 Yoshua Bengio Canada 476k citations
  2. 2 Daniel J. Kahneman United States 395k citations
  3. 3 Amos Tversky United States 327k citations
  4. 4 Eugene F. Fama United States 262k citations
  5. 5 Bruce Leonard Miller United States 196k citations
  6. 6 Michael I. Jordan United States 182k citations
  7. 7 Kalyanmoy Deb United States 171k citations
  8. 8 H. Vincent Poor United States 165k citations
  9. 9 David L. Donoho United States 154k citations
  10. 10 Bernhard Schölkopf Germany 148k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Risk and Portfolio Optimization?

The most cited paper in Risk and Portfolio Optimization is "Coherent Measures of Risk" (Philippe Artzner, Freddy Delbaen, Jean‐Marc Eber et al., 1999), with 9,137 citations. Next come "Optimum consumption and portfolio rules in a continuous-time model" (6,223) and "The Price of Robustness" (4,567).

Most cited papers
#PaperReleasedCitations
1 Coherent Measures of Risk Philippe Artzner, Freddy Delbaen, Jean‐Marc Eber et al. · Mathematical Finance Open access Jul 1999 9,137
2 Optimum consumption and portfolio rules in a continuous-time model Robert C. Merton · Journal of Economic Theory Dec 1971 6,223
3 The Price of Robustness Dimitris Bertsimas, Melvyn Sim · Operations Research Feb 2004 4,567
4 Increasing risk: I. A definition Michael Rothschild, Joseph E. Stiglitz · Journal of Economic Theory Sep 1970 3,940
5 Conditional value-at-risk for general loss distributions R. TYRRELL ROCKAFELLAR, Stan Uryasev · Journal of Banking & Finance Jul 2002 3,758
All 100 most cited papers, with filters and sorting

Where is Risk and Portfolio Optimization research done?

The largest centres of Risk and Portfolio Optimization research in 2022-now are Beijing (China), Shanghai (China), Nanjing (China) and Hong Kong (China). Among places with at least 20 works in it, it is an unusually large share of all research in Waterloo and Hong Kong.

Largest cities, 2022-now

  1. 1 BeijingChina 122 works
  2. 2 ShanghaiChina 62 works
  3. 3 NanjingChina 52 works
  4. 4 Hong KongChina 43 works
  5. 5 GuangzhouChina 43 works
  6. 6 JinanChina 39 works
  7. 7 LondonUnited Kingdom 38 works
  8. 8 New YorkUnited States 35 works
  9. 9 ParisFrance 33 works
  10. 10 TehranIran 32 works

Where it is the local speciality

  1. WaterlooCA · 22.0 works11×
  2. Hong KongCN · 42.8 works4.5×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Risk and Portfolio Optimization than the world average.

See Risk and Portfolio Optimization on the map

Where is the best place to study Risk and Portfolio Optimization?

Among universities, judged by research, Georgia Institute of Technology, Hong Kong Polytechnic University and Shandong University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 17.99%fractional works in this field (log) →share of work in the world top 10% →Georgia Institute of…Hong Kong Polytechni…Tsinghua UniversityShandong University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Georgia Institute of TechnologyUnited States 68.618.9%11.2×18 +47.6%
2Hong Kong Polytechnic UniversityChina 59.718.7%6.4×14 +78.3%
3Shandong UniversityChina 58.411.8%7.2×24 +38.3%
4Tsinghua UniversityChina 58.014.8%3.5×21 +68.6%
5University of WaterlooCanada 56.314.5%15.0×21 -6.0%
6Chinese University of Hong KongChina 50.519.4%6.3×12 -0.8%
7Massachusetts Institute of TechnologyUnited States 50.232.0%4.5×8 -37.8%
8Columbia UniversityUnited States 49.317.4%4.7×13 +6.4%
9University of TorontoCanada 48.116.5%2.8×14 +47.9%
10National University of SingaporeSingapore 47.415.9%3.9×12 +10.4%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Risk and Portfolio Optimization, country by country

Is Risk and Portfolio Optimization research growing?

Output in 2022-2025 was 16% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Risk and Portfolio Optimization.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Risk and Portfolio Optimization as a percentage of every work published that year, 0.0096% in 2024.

still counting0.0050%0.010%0.015%Risk and Portfolio Optimization0.013% in 202519801990200020102020

Fractional works of Risk and Portfolio Optimization over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Risk and Portfolio Optimization10.6% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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