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Optimization of Convex Risk Functions

Author

Listed:
  • Andrzej Ruszczyński

    () (Department of Management Science and Information Systems, Rutgers University, Piscataway, New Jersey 08854)

  • Alexander Shapiro

    () (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions, we develop new representation theorems for risk models, and optimality and duality theory for problems with convex risk functions.

Suggested Citation

  • Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
  • Handle: RePEc:inm:ormoor:v:31:y:2006:i:3:p:433-452
    DOI: 10.1287/moor.1050.0186
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    File URL: http://dx.doi.org/10.1287/moor.1050.0186
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    References listed on IDEAS

    as
    1. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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