Fast gradient descent method for Mean-CVaR optimization

We propose an iterative gradient descent algorithm for solving scenario-based Mean-CVaR portfolio selection problem. The algorithm is fast and does not require any LP solver. It also has efficiency advantage over the LP approach for large scenario size.

[1]  A. Meucci,et al.  Beyond Black-Litterman: Views on Non-Normal Markets , 2005 .

[2]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[3]  Maria Grazia Speranza,et al.  Semi-Absolute Deviation Rule for Mutual Funds Portfolio Selection , 2003, Ann. Oper. Res..

[4]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[5]  R. Rockafellar,et al.  Deviation Measures in Risk Analysis and Optimization , 2002 .

[6]  R. Rockafellar,et al.  Generalized Deviations in Risk Analysis , 2004 .

[7]  Panos M. Pardalos,et al.  Financial Engineering, E-commerce and Supply Chain , 2010 .

[8]  T. Coleman,et al.  Minimizing CVaR and VaR for a portfolio of derivatives , 2006 .

[9]  R. Mansini,et al.  A comparison of MAD and CVaR models with real features , 2008 .

[10]  Donald I. Rogers Make your income count , 1959 .

[11]  Suleyman Basak,et al.  Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices , 1999 .

[12]  W. Sharpe Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios , 1971 .

[13]  Hans-Jakob Lüthi,et al.  Convex risk measures for portfolio optimization and concepts of flexibility , 2005, Math. Program..

[14]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[15]  Yiannis A. Koskosidis,et al.  A Scenario-Based Approach to Active Asset Allocation , 1997 .

[16]  H. Konno,et al.  Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market , 1991 .

[17]  Stan Uryasev,et al.  Optimality conditions in portfolio analysis with general deviation measures , 2005, Math. Program..

[18]  G. Pflug,et al.  Value-at-Risk in Portfolio Optimization: Properties and Computational Approach ⁄ , 2005 .

[19]  A. Meucci Risk and asset allocation , 2005 .

[20]  Robert B. Litterman,et al.  Asset Allocation , 1991 .

[21]  Helmut Mausser,et al.  ALGORITHMS FOR OPTIMIZATION OF VALUE­ AT-RISK* , 2002 .

[22]  V. Agarwal,et al.  Risks and Portfolio Decisions Involving Hedge Funds , 2004 .

[23]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .