메뉴 건너뛰기




Volumn 59, Issue 4, 2011, Pages 847-865

Tight bounds for some risk measures, with applications to robust portfolio selection

Author keywords

Chebyshev inequality; Portfolio selection; Robust optimization; S shaped function

Indexed keywords

CHEBYSHEV INEQUALITIES; CONDITIONAL VALUE-AT-RISK; EXPECTED UTILITY; EXPECTED VALUES; INVESTMENT RETURNS; LOWER PARTIAL MOMENTS; NP-HARD; PORTFOLIO MODEL; PORTFOLIO SELECTION; PORTFOLIO SELECTION MODELS; PORTFOLIO SELECTION PROBLEMS; PROSPECT THEORY; QUADRATIC FUNCTION; RANDOM DISTRIBUTION; RISK MEASURES; ROBUST MODELS; ROBUST OPTIMIZATION; S-SHAPED; SECOND ORDERS; SEMI-DEFINITE PROGRAMMING; SINGLE STAGE; TIGHT BOUND; VALUE AT RISK; VALUE FUNCTIONS; VARIANCE ESTIMATION;

EID: 80053268411     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1110.0950     Document Type: Article
Times cited : (112)

References (45)
  • 2
    • 31144450867 scopus 로고
    • Optimal rules for ordering uncertain prospects
    • Bawa, V. S. 1975. Optimal rules for ordering uncertain prospects. J. Financial Econom. 2 (1) 95-121.
    • (1975) J. Financial Econom. , vol.2 , Issue.1 , pp. 95-121
    • Bawa, V.S.1
  • 4
    • 0003878614 scopus 로고    scopus 로고
    • Lectures on modern convex optimization: Analysis, algorithms, and engineering applications
    • Society for Industrial and Applied Mathematics, Philadelphia
    • Ben-Tal, A., A. Nemirovski. 2001. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics, Philadelphia.
    • (2001) MPS/SIAM Series on Optimization
    • Ben-Tal, A.1    Nemirovski, A.2
  • 5
    • 77955904315 scopus 로고    scopus 로고
    • A soft robust approach to optimization under ambiguity
    • Ben-Tal, A., D. Bertsimas, D. B. Brown. 2010. A soft robust approach to optimization under ambiguity. Oper. Res. 58 (4, Part 2) 1220-1234.
    • (2010) Oper. Res. , vol.58 , Issue.2-4 PART , pp. 1220-1234
    • Ben-Tal, A.1    Bertsimas, D.2    Brown, D.B.3
  • 6
    • 14844327381 scopus 로고    scopus 로고
    • Adjustable robust solutions of uncertain linear programs
    • DOI 10.1007/s10107-003-0454-y
    • Ben-Tal, A., A. Goryashko, E. Guslitzer, A. Nemirovski. 2004. Adjustable robust solutions of uncertain linear programs. Math. Programming 99 (2) 351-376. (Pubitemid 40871727)
    • (2004) Mathematical Programming , vol.99 , Issue.2 , pp. 351-376
    • Ben-Tal, A.1    Goryashko, A.2    Guslitzer, E.3    Nemirovski, A.4
  • 7
    • 0036508521 scopus 로고    scopus 로고
    • On the relation between option and stock prices: A convex optimization approach
    • Bertsimas, D., I. Popescu. 2002. On the relation between option and stock prices: A convex optimization approach. Oper. Res. 50 (2) 358-374. (Pubitemid 34721185)
    • (2002) Operations Research , vol.50 , Issue.2 , pp. 358-374
    • Bertsimas, D.1    Popescu, I.2
  • 8
    • 23844499733 scopus 로고    scopus 로고
    • Optimal inequalities in probability theory: A convex optimization approach
    • DOI 10.1137/S1052623401399903
    • Bertsimas, D., I. Popescu. 2005. Optimal inequality in probability theory: A convex optimization approach. SIAM J. Optim. 15 (3) 780-804. (Pubitemid 41156915)
    • (2005) SIAM Journal on Optimization , vol.15 , Issue.3 , pp. 780-804
    • Bertsimas, D.1    Popescu, I.2
  • 9
    • 0346808738 scopus 로고
    • Intorno ad un teorema fondamentale della teoria del rischio
    • Cantelli, F. P. 1910. Intorno ad un teorema fondamentale della teoria del rischio. Boll. Assoc. Attuar. Ital. (Milan) 1-23.
    • (1910) Boll. Assoc. Attuar. Ital. (Milan) , pp. 1-23
    • Cantelli, F.P.1
  • 10
    • 80053227547 scopus 로고    scopus 로고
    • When all risk-adjusted performance measures are the same: In praise of the Sharpe ratio
    • Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong
    • Chen, L., S. He, S. Zhang. 2007. When all risk-adjusted performance measures are the same: In praise of the Sharpe ratio, Technical Report SEEM2007-09, Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong.
    • (2007) Technical Report SEEM2007-09
    • Chen, L.1    He, S.2    Zhang, S.3
  • 12
    • 0031536271 scopus 로고    scopus 로고
    • Robust solutions to least-square problems with uncertain data
    • El Ghaoui, L., H. Lebret. 1997. Robust solutions to least-square problems with uncertain data. SIAM J. Matrix Anal. Appl. 18 (4) 1035-1064.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , Issue.4 , pp. 1035-1064
    • El Ghaoui, L.1    Lebret, H.2
  • 13
    • 4344618310 scopus 로고    scopus 로고
    • Worst-case value-at-risk and robust portfolio optimization: A conic programming approach
    • El Ghaoui, L., M. Oks, F. Oustry. 2003. Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. 51 (4) 543-556.
    • (2003) Oper. Res. , vol.51 , Issue.4 , pp. 543-556
    • El Ghaoui, L.1    Oks, M.2    Oustry, F.3
  • 14
    • 0000096680 scopus 로고
    • Mean-risk analysis with risk associated with belowtarget returns
    • Fishburn, P. C. 1977. Mean-risk analysis with risk associated with belowtarget returns. Amer. Econom. Rev. 67 (2) 116-126.
    • (1977) Amer. Econom. Rev. , vol.67 , Issue.2 , pp. 116-126
    • Fishburn, P.C.1
  • 15
    • 0038300035 scopus 로고    scopus 로고
    • Robust portfolio selection problem
    • Goldfarb, D., G. Iyengar. 2003. Robust portfolio selection problem. Math. Oper. Res. 28 (1) 1-38.
    • (2003) Math. Oper. Res. , vol.28 , Issue.1 , pp. 1-38
    • Goldfarb, D.1    Iyengar, G.2
  • 16
    • 80053239525 scopus 로고    scopus 로고
    • CVX: MATLAB software for disciplined convex programming
    • Grant, M., S. Boyd. 2011. CVX: MATLAB software for disciplined convex programming. http://cvxr.com/cvx/.
    • (2011) Http://cvxr.com/cvx/.
    • Grant, M.1    Boyd, S.2
  • 18
    • 63349096736 scopus 로고    scopus 로고
    • Bounding probability of small deviation: A fourth moment approach
    • Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong
    • He, S., J. Zhang, S. Zhang. 2007. Bounding probability of small deviation: A fourth moment approach. Technical Report SEEM2007-09, Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong.
    • (2007) Technical Report SEEM2007-09
    • He, S.1    Zhang, J.2    Zhang, S.3
  • 19
    • 34347391899 scopus 로고    scopus 로고
    • A control approach to robust utility maximization with logarithmic utility and time-consistent penalties
    • DOI 10.1016/j.spa.2006.11.005, PII S0304414906001748
    • Hernández-Hernández, D., A. Schied. 2007. A control approach to robust utility maximization with logarithmic utility and time consistent penalties. Stochastic Processes and Their Appl. 117 (8) 980-1000. (Pubitemid 47023026)
    • (2007) Stochastic Processes and their Applications , vol.117 , Issue.8 , pp. 980-1000
    • Hernandez-Hernandez, D.1    Schied, A.2
  • 20
    • 25444493818 scopus 로고    scopus 로고
    • Robust dynamic programming
    • DOI 10.1287/moor.1040.0129
    • Iyengar, G. 2005. Robust dynamic programming. Math. Oper. Res. 30 (2) 257-280. (Pubitemid 43126832)
    • (2005) Mathematics of Operations Research , vol.30 , Issue.2 , pp. 257-280
    • Iyengar, G.N.1
  • 21
    • 0000125532 scopus 로고
    • Prospect theory: An analysis of decisions under risk
    • Kahneman, D., A. Tversky. 1979. Prospect theory: An analysis of decisions under risk. Econometrica 43 263-291.
    • (1979) Econometrica , vol.43 , pp. 263-291
    • Kahneman, D.1    Tversky, A.2
  • 22
    • 0034347106 scopus 로고    scopus 로고
    • Optimal dynamic portfolio selection: Multiperiod mean-variance formulation
    • Li, D., W. Ng. 2000. Optimal dynamic portfolio selection: Multiperiod mean-variance formulation. Math. Finance 10 (3) 387-406.
    • (2000) Math. Finance , vol.10 , Issue.3 , pp. 387-406
    • Li, D.1    Ng, W.2
  • 23
    • 45949116982 scopus 로고
    • Semiparametric upper bounds for option prices and expected payoffs
    • Lo, A. 1987. Semiparametric upper bounds for option prices and expected payoffs. J. Financial Econom. 19 (2) 373-388.
    • (1987) J. Financial Econom. , vol.19 , Issue.2 , pp. 373-388
    • Lo, A.1
  • 26
    • 84995186518 scopus 로고
    • Portfolio selection
    • Markowitz, H. M. 1952. Portfolio selection. J. Finance 7 (1) 79-91.
    • (1952) J. Finance , vol.7 , Issue.1 , pp. 79-91
    • Markowitz, H.M.1
  • 28
    • 35448930268 scopus 로고    scopus 로고
    • A mean-variance bound for a threepiece linear function
    • Natarajan, K., L. Zhou. 2007. A mean-variance bound for a threepiece linear function. Probab. Engrg. Informational Sci. 21 (4) 611-621.
    • (2007) Probab. Engrg. Informational Sci. , vol.21 , Issue.4 , pp. 611-621
    • Natarajan, K.1    Zhou, L.2
  • 29
    • 41549090406 scopus 로고    scopus 로고
    • Incorporating asymmetric distributional information in robust value-at-risk optimization
    • DOI 10.1287/mnsc.1070.0769
    • Natarajan, K., D. Pachamanova, M. Sim. 2008. Incorporating asymmetric distributional information in robust value-at-risk optimization. Management Sci. 54 (3) 573-585. (Pubitemid 351463135)
    • (2008) Management Science , vol.54 , Issue.3 , pp. 573-585
    • Natarajan, K.1    Pachamanova, D.2    Sim, M.3
  • 30
    • 77953593241 scopus 로고    scopus 로고
    • Tractable robust expected utility and risk models for portfolio optimization
    • Natarajan, K., M. Sim, J. Uichanco. 2010. Tractable robust expected utility and risk models for portfolio optimization. Math. Finance 20 (4) 695-731.
    • (2010) Math. Finance , vol.20 , Issue.4 , pp. 695-731
    • Natarajan, K.1    Sim, M.2    Uichanco, J.3
  • 31
    • 10044286551 scopus 로고    scopus 로고
    • Paper No. 1997049, Center for Operations Research and Econometrics CORE, Université Catholique de Louvain, Belgium
    • Nesterov, Y. 1997. Structure of non-negative polynomial and optimization problems. Paper No. 1997049, Center for Operations Research and Econometrics (CORE), Université Catholique de Louvain, Belgium.
    • (1997) Structure of Non-negative Polynomial and Optimization Problems
    • Nesterov, Y.1
  • 32
    • 0003254248 scopus 로고
    • Interior-point Polynomial Algorithms in Convex Programming
    • Society for Industrial and Applied Mathematics, Philadelphia
    • Nesterov, Y., A. Nemirovski. 1994. Interior-Point Polynomial Algorithms in Convex Programming. Studies in Applied and Numerical Mathematics. Society for Industrial and Applied Mathematics, Philadelphia.
    • (1994) Studies in Applied and Numerical Mathematics
    • Nesterov, Y.1    Nemirovski, A.2
  • 33
    • 14344250395 scopus 로고    scopus 로고
    • Robust control of Markov decision processes with uncertain transition matrices
    • DOI 10.1287/opre.1050.0216
    • Nilim, A., L. El Ghaoui. 2005. Robust solutions to Markov decision problems with uncertain transition matrices. Oper. Res. 53 (5) 780-798. (Pubitemid 41525849)
    • (2005) Operations Research , vol.53 , Issue.5 , pp. 780-798
    • Nilim, A.1    Ghaoui, L.E.2
  • 34
    • 4244033129 scopus 로고    scopus 로고
    • Ph. D. dissertation, Applied Mathematics Department and Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA
    • Popescu, I. 1999. Applications of optimization in probability, finance and revenue management. Ph. D. dissertation, Applied Mathematics Department and Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA.
    • (1999) Applications of Optimization in Probability, Finance and Revenue Management
    • Popescu, I.1
  • 35
    • 31144445576 scopus 로고    scopus 로고
    • A semidefinite programming approach to optimal-moment bounds for convex classes of distributions
    • DOI 10.1287/moor.1040.0137
    • Popescu, I. 2005. A semidefinite programming approach to optimal moment bounds for convex classes of distributions. Math. Oper. Res. 50 (3) 632-657. (Pubitemid 43134194)
    • (2005) Mathematics of Operations Research , vol.30 , Issue.3 , pp. 632-657
    • Popescu, I.1
  • 36
    • 34247539626 scopus 로고    scopus 로고
    • Robust mean-covariance solutions for stochastic optimization
    • DOI 10.1287/opre.1060.0353
    • Popescu, I. 2007. Robust mean-covariance solutions for stochastic optimization. Oper. Res. 55 (1) 98-112. (Pubitemid 46663476)
    • (2007) Operations Research , vol.55 , Issue.1 , pp. 98-112
    • Popescu, I.1
  • 37
    • 0002062038 scopus 로고    scopus 로고
    • Optimization of conditional valueat-risk
    • Rockafellar, R. T., S. Uryasev. 2000. Optimization of conditional valueat-risk. J. Risk 2 (3) 21-41.
    • (2000) J. Risk , vol.2 , Issue.3 , pp. 21-41
    • Rockafellar, R.T.1    Uryasev, S.2
  • 38
    • 0036076694 scopus 로고    scopus 로고
    • Conditional value-at-risk for general loss distributions
    • Rockafellar, R. T., S. Uryasev. 2002. Conditional value-at-risk for general loss distributions. J. Banking Finance 26 (7) 1443-1471.
    • (2002) J. Banking Finance , vol.26 , Issue.7 , pp. 1443-1471
    • Rockafellar, R.T.1    Uryasev, S.2
  • 39
    • 0001567393 scopus 로고
    • Safety first and the holding of assets
    • Roy, A. D. 1952. Safety first and the holding of assets. Econometrica 20 (3) 431-449.
    • (1952) Econometrica , vol.20 , Issue.3 , pp. 431-449
    • Roy, A.D.1
  • 40
    • 0002693448 scopus 로고
    • A min-max solution of an inventory problem
    • K. J. Arrow, S. Karlin and H. E. Scarf eds, Stanford University Press, Stanford, CA
    • Scarf, H. 1958. A min-max solution of an inventory problem. K. J. Arrow, S. Karlin and H. E. Scarf eds. Studies in the Mathematical Theory of Inventory and Production. Stanford University Press, Stanford, CA, 201-209.
    • (1958) Studies in the Mathematical Theory of Inventory and Production , pp. 201-209
    • Scarf, H.1
  • 41
    • 0033296299 scopus 로고    scopus 로고
    • Using seDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • Sturm, J. F. 1999. Using seDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Software 11 (12) 625-653.
    • (1999) Optim. Methods Software , vol.11 , Issue.12 , pp. 625-653
    • Sturm, J.F.1
  • 42
    • 0038386380 scopus 로고    scopus 로고
    • On cones of nonnegative quadratic functions
    • Sturm, J. F., S. Zhang. 2003. On cones of nonnegative quadratic functions. Math. Oper. Res. 28 (2) 246-267.
    • (2003) Math. Oper. Res. , vol.28 , Issue.2 , pp. 246-267
    • Sturm, J.F.1    Zhang, S.2
  • 43
    • 31744450082 scopus 로고
    • Advances in prospect theory: Cumulative representation of uncertainty
    • Tversky, A., D. Kahneman. 1992. Advances in prospect theory: Cumulative representation of uncertainty. J. Risk Uncertainty 5 147-176.
    • (1992) J. Risk Uncertainty , vol.5 , pp. 147-176
    • Tversky, A.1    Kahneman, D.2
  • 44
    • 70350235055 scopus 로고    scopus 로고
    • Worst-case conditional value-at-risk with application to robust portfolio management
    • Zhu, S. S., M. Fukushima. 2009. Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. 57 (5) 1155-1168.
    • (2009) Oper. Res. , vol.57 , Issue.5 , pp. 1155-1168
    • Zhu, S.S.1    Fukushima, M.2
  • 45
    • 31144475041 scopus 로고    scopus 로고
    • A conic programming approach to generalized tchebycheff inequalities
    • DOI 10.1287/moor.1040.0124
    • Zuluaga, L., J. Peña. 2005. A conic programming approach to generalized Tchebycheff inequalities. Math. Oper. Res. 30 (2) 369-388. (Pubitemid 43126837)
    • (2005) Mathematics of Operations Research , vol.30 , Issue.2 , pp. 369-388
    • Zuluaga, L.F.1    Pena, J.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.