zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set. (English) Zbl 1208.91136
Summary: The “separable” uncertainty sets have been widely used in robust portfolio selection models [e.g., see D. Goldfarb and G. Iyengar, Math. Oper. Res. 28, No. 1, 1–38 (2003; Zbl 1082.90082)]. For these uncertainty sets, each type of uncertain parameters (e.g., mean and covariance) has its own uncertainty set. As addressed in [Z. Lu, “A new cone programming approach for robust portfolio selection”, technical report, Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada (2006); “Robust portfolio selection based on a joint ellipsoidal uncertainty set”, Optim. Methods Softw. 26, No. 1, 89–104 (2009)], these “separable” uncertainty sets typically share two common properties: (i) their actual confidence level, namely, the probability of uncertain parameters falling within the uncertainty set is unknown, and it can be much higher than the desired one; and (ii) they are fully or partially box-type. The associated consequences are that the resulting robust portfolios can be too conservative, and moreover, they are usually highly non-diversified as observed in the computational experiments conducted in this paper and [R. H. Tütüncü and M. Koenig, Ann. Oper. Res. 132, 157–187 (2004; Zbl 1090.90125)]. To combat these drawbacks, the author of this paper introduced a “joint” ellipsoidal uncertainty set [Lu, loc. cit.] and showed that it can be constructed as a confidence region associated with a statistical procedure applied to estimate the model parameters. For this uncertainty set, the author showed in [Lu, loc. cit.] that the corresponding robust maximum risk-adjusted return (RMRAR) model can be reformulated and solved as a cone programming problem. In this paper, we conduct computational experiments to compare the performance of the robust portfolios determined by the RMRAR models with our “joint” uncertainty set [Lu, loc. cit.] and Goldfarb and Iyengar’s “separable” uncertainty set proposed in the seminal paper [Goldfarb, loc. cit.]. Our computational results demonstrate that our robust portfolio outperforms Goldfarb and Iyengar’s in terms of wealth growth rate and transaction cost, and moreover, ours is fairly diversified, but Goldfarb and Iyengar’s is surprisingly highly non-diversified.

MSC:
91G10Portfolio theory
91G60Numerical methods in mathematical finance
90C20Quadratic programming
90C22Semidefinite programming
Software:
SeDuMi
References:
[1]Ben-Tal A., Margalit T., Nemirovski A.: Robust modeling of multi-stage portfolio problems. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds) High Performance Optimization, pp. 303–328. Kluwer Academic Press, Dordrecht (2000)
[2]El Ghaoui L., Oks M., Outstry F.: Worst-case value-at-risk and robust portfolio optimization: a conic programming approach. Oper. Res. 51, 543–556 (2003) · Zbl 1165.91397 · doi:10.1287/opre.51.4.543.16101
[3]Erdoğan, E., Goldfarb, D., Iyengar, G.: Robust portfolio management. manuscript, Department of Industrial Engineering and Operations Research, Columbia University, New York 10027-6699, November (2004)
[4]Goldfarb D., Iyengar G.: Robust portfolio selection problems. Math. Oper. Res. 28, 1–38 (2003) · Zbl 1082.90082 · doi:10.1287/moor.28.1.1.14260
[5]Lu, Z.: A new cone programming approach for robust portfolio selection. technical report, Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada, December (2006)
[6]Lu, Z.: Robust portfolio selection based on a joint ellipsoidal uncertainty set. manuscript, Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada, May (2008)
[7]Markowitz H.M.: Portfolio selection. J. Finance 7, 77–91 (1952) · doi:10.2307/2975974
[8]Michaud R.O.(1998) Efficient asset management: a practical guide to stock portfolio management and asset allocation. Financial Management Association, Survey and Synthesis. HBS Press, Boston
[9]Sturm J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11, 625–653 (1999) · Zbl 0973.90526 · doi:10.1080/10556789908805766
[10]Tütüncü R.H., Koenig M.: Robust asset allocation. Ann. Oper. Res. 132, 157–187 (2004) · Zbl 1090.90125 · doi:10.1023/B:ANOR.0000045281.41041.ed
[11]Zhu, S., Fukushima, M.: Worst-case conditional value-at-risk with application to robust portfolio management, technical report 2005–2006, Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8501, Japan, July (2005). (Accepted in Operations Research)