A multiproduct risk-averse newsvendor with law-invariant coherent measures of risk

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Abstract

We consider a multiproduct risk-averse newsvendor under the law-invariant coherent measures of risk. We first establish several fundamental properties of the model regarding the convexity of the problem, the symmetry of the solution, and the impact of risk aversion. Specifically, we show that for identical products with independent demands, increased risk aversion leads to decreased orders. For a large but finite number of heterogeneous products with independent demands, we derive closed-form approximations for the optimal order quantities. The approximations are as simple to compute as the classical risk-neutral solutions. We also show that the risk-neutral solution is asymptotically optimal as the number of products tends to be infinity, and thus risk aversion has no impact in the limit. For a risk-averse newsvendor with dependent demands, we show that positively (negatively) dependent demands lead to lower (higher) optimal order quantities than independent demands. Using a numerical study, we examine the convergence rates of the approximations and develop additional insights into the interplay between dependent demands and risk aversion.

Original languageEnglish (US)
Pages (from-to)346-364
Number of pages19
JournalOperations Research
Volume59
Issue number2
DOIs
StatePublished - Mar 2011

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Management Science and Operations Research

Keywords

  • Coherent measures of risk
  • Diversification
  • Multiple products
  • Newsvendor; risk aversion
  • Portfolio

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