A copula-based heuristic for scenario generation

This paper presents a new heuristic for generating scenarios for two-stage stochastic programs. The method uses copulas to describe the dependence between the marginal distributions, instead of the more common correlations. The heuristic is then tested on a simple portfolio-selection model, and compared to two other scenario-generation methods.

[1]  Stan Uryasev,et al.  Calibrating risk preferences with the generalized capital asset pricing model based on mixed conditional value-at-risk deviation , 2012 .

[2]  Michal Kaut,et al.  A Heuristic for Moment-Matching Scenario Generation , 2003, Comput. Optim. Appl..

[3]  F. Longin,et al.  Extreme Correlation of International Equity Markets , 2000 .

[4]  S. Wallace,et al.  Evaluation of scenario-generation methods for stochastic programming , 2007 .

[5]  Tim Hultberg.  FLOPC++ An Algebraic Modeling Language Embedded in C++ , 2006, OR.

[6]  R. Clemen,et al.  Correlations and Copulas for Decision and Risk Analysis , 1999 .

[7]  Andrew J. Patton.  On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation , 2002 .

[8]  R. Nelsen.  An Introduction to Copulas , 1998 .

[9]  Michal Kaut,et al.  Shape-based scenario generation using copulas , 2011, Comput. Manag. Sci..

[10]  Jitka Dupacová,et al.  Scenarios for Multistage Stochastic Programs , 2000, Ann. Oper. Res..

[11]  J. Rosenberg.  Non-Parametric Pricing of Multivariate Contingent Claims , 2003 .

[12]  Eric Bouyé,et al.  Copulas for Finance - A Reading Guide and Some Applications , 2000 .

[13]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[14]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[15]  John Forrest,et al.  CBC User Guide , 2005 .

[16]  Ling Hu.  Dependence patterns across financial markets: a mixed copula approach , 2006 .

[17]  S. Wallace,et al.  Product variety arising from hedging in the fashion supply chains , 2008 .

[18]  A. Sklar,et al.  Random variables, distribution functions, and copulas---a personal look backward and forward , 1996 .

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

[20]  Andrew J. Patton.  Applications of copula theory in financial econometrics , 2002 .