北大中文核心期刊
中国科学引文数据库(CSCD)来源期刊
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入选数学领域高质量科技期刊
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运筹学学报(中英文) ›› 2025, Vol. 29 ›› Issue (3): 135-159.doi: 10.15960/j.cnki.issn.1007-6093.2025.03.007
所属专题: 第九届中国运筹学会科学技术奖获奖者专辑
• 第九届中国运筹学会科学技术奖获奖者专辑 • 上一篇 下一篇
收稿日期:2025-03-21
出版日期:2025-09-15
发布日期:2025-09-09
通讯作者:
胡照林
E-mail:russell@tongji.edu.cn
基金资助:Received:2025-03-21
Online:2025-09-15
Published:2025-09-09
Contact:
Zhaolin HU
E-mail:russell@tongji.edu.cn
摘要:
风险管理在不确定性环境决策中常常起着重要作用。在量化风险管理中,评估和优化风险指标需要高效的计算技术和可靠的理论保证。本文介绍量化风险管理的几个主题,并回顾关于这些主题的一些研究和进展。我们考虑几个风险指标并研究涉及这些指标的决策模型,主要关注相关的计算技术和理论性质。我们说明随机优化作为一种强大的工具,可以用来有效处理这些问题。
中图分类号:
胡照林. 基于随机优化的量化风险管理的一些研究[J]. 运筹学学报(中英文), 2025, 29(3): 135-159.
Zhaolin HU. Some studies on stochastic optimization based quantitative risk management[J]. Operations Research Transactions, 2025, 29(3): 135-159.
| 1 | GlassermanP.Monte Carlo Methods in Financial Engineering[M].New York:Springer,2004. |
| 2 |
RuszczyńskiA,ShapiroA.Optimization of convex risk functions[J].Mathematics of Operations Research,2006,31(3):433-452.
doi: 10.1287/moor.1050.0186 |
| 3 | ShapiroA,DentchevaD,RuszczyńskiA.Lectures on Stochastic Programming: Modeling and Theory[M].Philadelphia:SIAM,2014. |
| 4 | JorionP.Value at Risk[M].New York:McGraw-Hill,2006. |
| 5 |
RockafellarR T,UryasevS.Optimization of conditional value-at-risk[J].The Journal of Risk,2000,2(3):21-41.
doi: 10.21314/JOR.2000.038 |
| 6 | HongL J,HuZ,LiuG.Monte Carlo methods for value-at-risk and conditional value-at-risk: A review[J].ACM Transactions on Modeling and Computer Simulation,2014,24(4):Article 22. |
| 7 |
ArtznerP,DelbaenF,EberJ M,et al.Coherent measures of risk[J].Mathematical Finance,1999,9(3):203-228.
doi: 10.1111/1467-9965.00068 |
| 8 |
FÖllmerH,SchiedA.Convex measures of risk and trading constraints[J].Finance and Stochastics,2002,6,429-447.
doi: 10.1007/s007800200072 |
| 9 |
FrittelliM,GianinE R.Putting order in risk measures[J].Journal of Banking and Finance,2002,26(7):1473-1486.
doi: 10.1016/S0378-4266(02)00270-4 |
| 10 |
CharnesA,CooperW W,SymondsG H.Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil[J].Management Science,1958,4(3):235-263.
doi: 10.1287/mnsc.4.3.235 |
| 11 |
Ben-TalA,TeboulleM.Expected utility, penalty functions, and duality in stochastic nonlinear programming[J].Management Science,1986,32(11):1445-1466.
doi: 10.1287/mnsc.32.11.1445 |
| 12 |
Ben-Tal,A,TeboulleM.An old-new concept of convex risk measures: The optimized certainty equivalent[J].Mathematical Finance,2007,17(3):449-476.
doi: 10.1111/j.1467-9965.2007.00311.x |
| 13 | Hamm A M, Salfeld T, Weber S. Stochastic root finding for optimized certainty equivalents[C]//Proceedings of the 2013 Winter Simulation Conference, 2013: 922-932. |
| 14 | RockafellarR T,UryasevS.The fundamental risk quadrangle in risk management, optimization and statistical estimation[J].Surveys in Operations Research and Management Science,2013,18(1):33-53. |
| 15 |
RockafellarR T,RoysetJ O.Measures of residual risk with connections to regression, risk tracking, surrogate models, and ambiguity[J].SIAM Journal on Optimization,2015,25(2):1179-1208.
doi: 10.1137/151003271 |
| 16 |
DunkelJ,WeberS.Stochastic root finding and efficient estimation of convex risk measures[J].Operations Research,2010,58(5):1505-1521.
doi: 10.1287/opre.1090.0784 |
| 17 |
TrindadeA A,UryasevS,ShapiroA,et al.Financial prediction with constrained tail risk[J].Journal of Banking and Finance,2007,31(11):3524-3538.
doi: 10.1016/j.jbankfin.2007.04.014 |
| 18 | DurrettR.Probability: Theory and Examples[M].Cambridge:Cambridge University Press,2019. |
| 19 | HuberP J,RonchettiE M.Robust Statistics[M].New Jersey:John Wiley & Sons,2011. |
| 20 |
HongL J,LiuG.Simulating sensitivities of conditional value-at-risk[J].Management Science,2009,55(2):281-293.
doi: 10.1287/mnsc.1080.0901 |
| 21 |
GlynnP W,FanL,FuM C,et al.Central limit theorems for estimated functions at estimated points[J].Operations Research,2020,68(5):1557-1563.
doi: 10.1287/opre.2019.1922 |
| 22 |
KrokhmalP A.Higher moment coherent risk measures[J].Quantitative Finance,2007,7(4):373-387.
doi: 10.1080/14697680701458307 |
| 23 |
AlexanderS,ColemanT F,LiY.Minimizing CVaR and VaR for a portfolio of derivatives[J].Journal of Banking and Finance,2006,30(2):583-605.
doi: 10.1016/j.jbankfin.2005.04.012 |
| 24 |
HuZ,ZhangD.Utility-based shortfall risk: Efficient computations via Monte Carlo[J].Naval Research Logistics,2018,65(5):378-392.
doi: 10.1002/nav.21814 |
| 25 | Hegde V, Menon A S, Prashanth L A, et al. Online estimation and optimization of utility-based shortfall risk[J/OL].[2025-08-05]. Mathematics of Operations Research. https://doi.org/10.1287/moor.2022.0266. |
| 26 |
LuedtkeJ,AhmedS.A sample approximation approach for optimization with probabilistic constraints[J].SIAM Journal on Optimization,2008,19(2):674-699.
doi: 10.1137/070702928 |
| 27 |
PagnoncelliB K,AhmedS,ShapiroA.Sample average approximation method for chance constrained programming: Theory and applications[J].Journal of Optimization Theory and Applications,2009,142,399-416.
doi: 10.1007/s10957-009-9523-6 |
| 28 |
CalafioreG,CampiM C.Uncertain convex programs: Randomized solutions and confidence levels[J].Mathematical Programming,2005,102,25-46.
doi: 10.1007/s10107-003-0499-y |
| 29 |
CalafioreG,CampiM C.The scenario approach to robust control design[J].IEEE Transactions on Automatic Control,2006,51(5):742-753.
doi: 10.1109/TAC.2006.875041 |
| 30 |
De FariasD P,Van RoyB.On constraint sampling in the linear programming approach to approximate dynamic programming[J].Mathematics of Operations Research,2004,29(3):462-478.
doi: 10.1287/moor.1040.0094 |
| 31 |
KüçükyavuzS,JiangR.Chance-constrained optimization under limited distributional information: A review of reformulations based on sampling and distributional robustness[J].EURO Journal on Computational Optimization,2022,10,100030.
doi: 10.1016/j.ejco.2022.100030 |
| 32 |
HenrionR,MÖllerA.A gradient formula for linear chance constraints under Gaussian distribution[J].Mathematics of Operations Research,2012,37(3):475-488.
doi: 10.1287/moor.1120.0544 |
| 33 |
van AckooijW,HenrionR.Gradient formulae for nonlinear probabilistic constraints with Gaussian and Gaussian-like distributions[J].SIAM Journal on Optimization,2014,24(4):1864-1889.
doi: 10.1137/130922689 |
| 34 |
HongL J.Estimating quantile sensitivities[J].Operations Research,2009,57(1):118-130.
doi: 10.1287/opre.1080.0531 |
| 35 |
HongL J,JiangG.Gradient and hessian of joint probability function with applications on chance-constrained programs[J].Journal of the Operations Research Society of China,2017,5,431-455.
doi: 10.1007/s40305-017-0154-6 |
| 36 | Feng G, Liu G. Conditional Monte Carlo: A change-of-variables approach[EB/OL].[2025-08-05]. https://arxiv.org/abs/1603.06378. |
| 37 |
HongL J,YangY,ZhangL.Sequential convex approximations to joint chance constrained programs: A Monte Carlo approach[J].Operations Research,2011,59(3):617-630.
doi: 10.1287/opre.1100.0910 |
| 38 |
HuZ,HongL J,ZhangL.A smooth Monte Carlo approach to joint chance constrained program[J].IIE Transactions,2013,45(7):716-735.
doi: 10.1080/0740817X.2012.745205 |
| 39 |
ShanF,ZhangL,XiaoX.A smoothing function approach to joint chance-constrained programs[J].Journal of Optimization Theory and Applications,2014,163,181-199.
doi: 10.1007/s10957-013-0513-3 |
| 40 |
CuiY,LiuJ,PangJ S.Nonconvex and nonsmooth approaches for affine chance-constrained stochastic programs[J].Set-Valued and Variational Analysis,2022,30(3):1149-1211.
doi: 10.1007/s11228-022-00639-y |
| 41 |
Peña-OrdieresA,LuedtkeJ,WächterA.Solving chance-constrained problems via a smooth sample-based nonlinear approximation[J].SIAM Journal on Optimization,2020,30(3):2221-2250.
doi: 10.1137/19M1261985 |
| 42 |
HuZ,SunW,ZhuS.Chance constrained programs with Gaussian mixture models[J].IISE Transactions,2022,54(12):1117-1130.
doi: 10.1080/24725854.2021.2001608 |
| 43 | WeiJ,HuZ,LuoJ.Appointment scheduling optimization with chance constraints in a singleserver consultation system[J].Systems Engineering-Theory & Practice,2024,44(10):3400-3417. |
| 44 | WeiJ,HuZ,LuoJ,et al.Enhanced branch-and-bound algorithm for chance constrained programs with Gaussian mixture models[J].Annals of Operations Research,2024,338(2):1283-1315. |
| 45 | Pang X, Zhu S, Hu Z. Chance constrained program with quadratic randomness: A unified approach based on Gaussian mixture distribution[EB/OL].[2025-07-06]. arXiv:2303.00555v1. |
| 46 | GordyM B,JunejaS.Nested simulation in portfolio risk measurement[J].Management Science,2010,56(9):1658-1673. |
| 47 |
BroadieM,DuY,MoallemiC C.Risk estimation via regression[J].Operations Research,2015,63(5):1077-1097.
doi: 10.1287/opre.2015.1419 |
| 48 |
HongL J,JunejaS,LiuG.Kernel smoothing for nested estimation with application to portfolio risk measurement[J].Operations Research,2017,65(3):657-673.
doi: 10.1287/opre.2017.1591 |
| 49 |
ZhangK,LiuG,WangS.Bootstrap-based budget allocation for nested simulation[J].Operations Research,2022,70(2):1128-1142.
doi: 10.1287/opre.2020.2071 |
| 50 | WangW,WangY,ZhangX.Smooth nested simulation: Bridging cubic and square root convergence rates in high dimensions[J].Management Science,2024,70(2):9031-9057. |
| 51 | Liu G, Zhang K. A tutorial on nested simulation[C]//Proceedings of the 2024 Winter Simulation Conference, 2024: 1-15. |
| 52 |
HuZ,HongL J.Robust simulation with likelihood-ratio constrained input uncertainty[J].INFORMS Journal on Computing,2022,34(4):2350-2367.
doi: 10.1287/ijoc.2022.1169 |
| 53 |
KuhnD,ShafieeS,WiesemannW.Distributionally robust optimization[J].Acta Numerica,2025,34,579-804.
doi: 10.1017/S0962492924000084 |
| 54 | ZhuS,FukushimaM.Worst-case conditional value-at-risk with application to robust portfolio management[J].Operations Research,2009,57(5):1155-1168. |
| 55 | GuoS,XuH.Distributionally robust shortfall risk optimization model and its approximation[J].Mathematical Programming,2019,174(1):473-498. |
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