A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk

Sungyong Choi (), Andrzej Ruszczynski () and Yao Zhao ()
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Sungyong Choi: Division of Systems and Engineering Management, Nanyang Technological University, Singapore 639798
Yao Zhao: Department of Supply Chain Management and Marketing Sciences, Rutgers University, Newark, New Jersey 07102

Operations Research, 2011, vol. 59, issue 2, 346-364

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.

Keywords: multiple products; newsvendor; risk aversion; coherent measures of risk; diversification; portfolio (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (32)

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