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Multiperiod stochastic optimization problems with time-consistent risk constraints


Densing, Martin; Mayer, Janos (2012). Multiperiod stochastic optimization problems with time-consistent risk constraints. In: Klatte, Diethard; Lüthi, Hans-Jakob; Schmedders, Karl. Operations Research Proceedings 20122. Berlin Heidelberg: Springer, 521-526.

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.

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.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2012
Deposited On:28 Jan 2013 13:38
Last Modified:17 Feb 2018 00:57
Publisher:Springer
Series Name:Operations Research Proceedings
Number of Pages:6
ISSN:0721-5924
ISBN:978-3-642-29209-5
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/978-3-642-29210-1_83
Other Identification Number:merlin-id:7715

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