Worst-Case Value at Risk of Nonlinear Portfolios

References

• Acerbi C, Tasche D. On the coherence of expected shortfall. J. Banking Finance (2002) 26(7):1487–1503Crossref, Google Scholar
• Alizadeh F, Goldfarb D. Second-order cone programming. Math. Programming (2003) 95(1):3–51Crossref, Google Scholar
• Artzner P, Delbaen F, Eber J, Heath D. Coherent measures of risk. Math. Finance (1999) 9(3):203–228Crossref, Google Scholar
• Ben-Tal A, Nemirovski A. Robust convex optimization. Math. Oper. Res. (1998) 23(4):769–805Link, Google Scholar
• Ben-Tal A, Nemirovski A. Robust solutions of uncertain linear programs. Oper. Res. Lett. (1999) 25(1):1–13Crossref, Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A. Robust Optimization (2009) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Bertsimas D, Sim M. The price of robustness. Oper. Res. (2004) 52(1):35–53Link, Google Scholar
• Black F, Scholes M. The pricing of options and corporate liabilities. J. Political Econom. (1973) 81(3):637–654Crossref, Google Scholar
• Calafiore G, Topcu U, El Ghaoui L. Parameter estimation with expected and residual-at-risk criteria. Systems Control Lett. (2009) 58(1):39–46Crossref, Google Scholar
• Coval J, Shumway T. Expected option returns. J. Finance (2002) 56(3):983–1009Crossref, Google Scholar
• El Ghaoui L, Oks M, Oustry F. Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. (2003) 51(4):543–556Link, Google Scholar
• Gaivoronski A, Pflug G. Value-at-risk in portfolio optimization: Properties and computational approach. J. Risk (2005) 7(2):1–31Crossref, Google Scholar
• Jaschke S. The cornish-fisher expansion in the context of delta–gamma-normal approximations. J. Risk (2002) 4(4):33–53Crossref, Google Scholar
• Jorion P. Value-at-Risk: The New Benchmark for Managing Financial Risk (2001) (McGraw-Hill, New York) Google Scholar
• MacMillan L. Options as a Strategic Investment (1992) (Prentice Hall, Upper Saddle River, NJ) Google Scholar
• Markowitz H. Portfolio selection. J. Finance (1952) 7(1):77–91Google Scholar
• Mina J, Ulmer A. Delta–gamma four ways. (1999) . Technical report, RiskMetrics Group, New YorkGoogle Scholar
• Natarajan K, Pachamanova D, Sim M. Incorporating asymmetric distributional information in robust value-at-risk optimization. Management Sci. (2008) 54(3):573–585Link, Google Scholar
• Natarajan K, Pachamanova D, Sim M. Constructing risk measures from uncertainty sets. Oper. Res. (2009) 57(5):1129–1141Link, Google Scholar
• Natarajan K, Sim M, Uichanco J. Tractable robust expected utility and risk models for portfolio optimisation. Math. Finance (2010) 20(4):695–731Crossref, Google Scholar
• Pólik I, Terlaky T. A survey of the S-lemma. SIAM Rev. (2007) 49(3):371–481Crossref, Google Scholar
• Rockafellar R, Uryasev S. Optimization of conditional value-at-risk. J. Risk (2002) 2:21–41Crossref, Google Scholar
• Rustem B, Howe M. Algorithms for Worst-Case Design and Applications to Risk Management (2002) (Princeton University Press, Princeton, NJ) Google Scholar
• Tütüncü RH, Toh KC, Todd MJ. Solving semidefinite-quadratic-linear programs using SDPT3. Math. Programming Ser. B (2003) 95(2):189–217Crossref, Google Scholar
• Vandenberghe L, Boyd S. Semidefinite programming. SIAM Rev. (1996) 38(1):49–95Crossref, Google Scholar
• Ye Y. Interior Point Algorithms: Theory and Analysis (1997) (John Wiley & Sons, New York) Crossref, Google Scholar
• Zhu S, Fukushima M. Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. (2009) 57(5):1155–1168Link, Google Scholar
• Zymler S, Kuhn D, Rustem B. Distributionally robust joint chance constraints with second-order moment information. Math. Programming (2011a) . ePub ahead of print November 10, http://dx.doi.org/10.1007/s10107-011-0494-7Google Scholar
• Zymler S, Rustem B, Kuhn D. Robust portfolio optimization with derivative insurance guarantees. Eur. J. Oper. Res. (2011b) 210(2):410–424Crossref, Google Scholar