Stochastic programs and statistical data

Using statistical data instead of true underlying distributions in a stochastic optimizationproblem leads to an approximation error. We discuss how bounds for this error can be derivedfrom results on uniformity in the law of large numbers.

[1]  Roger J.-B. Wets,et al.  Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems , 1995, Ann. Oper. Res..

[2]  M. Talagrand The Glivenko-Cantelli Problem , 1987 .

[3]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[4]  Wlodzimierz Ogryczak,et al.  From stochastic dominance to mean-risk models: Semideviations as risk measures , 1999, Eur. J. Oper. Res..

[5]  Peter C. Fishburn,et al.  Stochastic Dominance and Moments of Distributions , 1980, Math. Oper. Res..

[6]  K. Arrow Essays in the theory of risk-bearing , 1958 .

[7]  J. Pratt RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

[8]  Alexander Shapiro,et al.  Quantitative stability in stochastic programming , 1994, Math. Program..

[9]  L. Devroye A Course in Density Estimation , 1987 .

[10]  J. Hull Options, futures, and other derivative securities , 1989 .

[11]  S. Yitzhaki Stochastic Dominance, Mean Variance, and Gini's Mean Difference , 1982 .

[12]  J. Grandell Aspects of Risk Theory , 1991 .

[13]  Yuri Ermoliev,et al.  Numerical techniques for stochastic optimization , 1988 .

[14]  Michael J. McNamara,et al.  Principles of risk management and insurance , 1978 .

[15]  Georg Ch. Pflug,et al.  Risk-Reshaping Contracts and Stochastic Optimization , 1996 .

[16]  Georg Ch. Pflug,et al.  On the Glivenko-Cantelli Problem in Stochastic Programming: Linear Recourse and Extensions , 1996, Math. Oper. Res..

[17]  Georg Ch. Pflug,et al.  Asymptotic Stochastic Programs , 1995, Math. Oper. Res..

[18]  M. Yaari,et al.  Uncertainty, information, and communication: Univariate and multivariate comparisons of risk aversion: a new approach , 1986 .

[19]  Bob Ritchie,et al.  Business Risk Management , 1993 .

[20]  Anna Nagurney,et al.  Foundations of Financial Economics , 1997 .

[21]  M. Talagrand Sharper Bounds for Gaussian and Empirical Processes , 1994 .

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