Robust Portfolio Selection Problems

@article{Goldfarb2003RobustPS,
  title={Robust Portfolio Selection Problems},
  author={Donald Goldfarb and Garud Iyengar},
  journal={Math. Oper. Res.},
  year={2003},
  volume={28},
  pages={1-38}
}
In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce "uncertainty structures" for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second-order cone programs… 
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References

SHOWING 1-10 OF 42 REFERENCES

Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach

The problem of computing and optimizing the worst-case VaR and various other partial information on the distribution, including uncertainty in factor models, support constraints, and relative entropy information can be cast as semidefinite programs.

The effect of estimation risk on optimal portfolio choice

An Empirical Bayes Approach to Efficient Portfolio Selection

  • P. FrostJ. Savarino
  • Economics, Computer Science
    Journal of Financial and Quantitative Analysis
  • 1986
This empirical Bayes method is shown to select portfolios whose performance is superior to that achieved, given the assumption of a noninformative prior or by using classical sample estimates.

Massaging mean-variance inputs: returns from alternative global investment strategies in the 1980s

This paper explores the impact of adjustments to the inputs on total returns, terminal wealth, and portfolio turnover in an unconstrained monthly mean-variance (MV) asset allocation over time. It is…

Computing efficient frontiers using estimated parameters

The tradeoff between estimation error and stationarity is investigated and a method for adjusting for the bias is suggested and a statistical test is proposed to check for nonstationarity in historical data.

Credit risk optimization with Conditional Value-at-Risk criterion

This paper examines a new approach for credit risk optimization based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value- at-Risks, also known as Mean Excess, Mean Shortfall, or Tail VaR.

Robust solutions of uncertain linear programs

Asset Allocation

nvestors create global bond portfolios for a variety of reasons: to diversify interest rate risk, to manage yield, to control exposure to foreign currencies, and to enlarge the universe of possible…

Beyond VaR: from measuring risk to managing risk

  • Helmut E. MausserD. Rosen
  • Economics
    Proceedings of the IEEE/IAFE 1999 Conference on Computational Intelligence for Financial Engineering (CIFEr) (IEEE Cat. No.99TH8408)
  • 1999
This paper examines tools for managing, as opposed to simply monitoring, a portfolio's value-at-risk (VaR), and reviews the parametric, or delta-normal versions of these tools and then extends them to the simulation based, or nonparametric case.

Robust Convex Optimization

If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.