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Multiperiod Stochastic Optimization Problems with Time-Consistent Risk Constraints

In: Operations Research Proceedings 2011

Author

Listed:
  • M. Densing

    (Energy Economics Group, Paul Scherrer Institute)

  • J. Mayer

    (University of Zurich)

Abstract

Coherent risk measures play an important role in building and solving optimization models for decision problems under uncertainty. We consider an extension to multiple time periods, where a risk-adjusted value for a stochastic process is recursively defined over the time steps, which ensures time consistency. A prominent example of a single-period coherent risk measure that is widely used in applications is Conditional-Value-at-Risk (CVaR). We show that a recursive calculation of CVaR leads to stochastic linear programming formulations. For the special case of the risk-adjusted value of a random variable at the time horizon, a lower bound is given. The possible integration of the risk-adjusted value into multi-stage mean-risk optimization problems is outlined.

Suggested Citation

  • M. Densing & J. Mayer, 2012. "Multiperiod Stochastic Optimization Problems with Time-Consistent Risk Constraints," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 521-526, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-29210-1_83
    DOI: 10.1007/978-3-642-29210-1_83
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