Risk Vulnerability and Mean-Variance Newsvendor Model with Background Risk

Abstract

The newsvendor model is a building block for inventory management under stochastic situation. This paper examines the effects of an additive and a multiplicative background risk separately on the optimal order quantity of a risk-averse newsvendor with Mean-Variance utility. We derive several unambiguous comparative statics results with the additive background risk with the use of the concept of the Mean-Variance vulnerability (Eichner [1]). Moreover, we introduce a multiplicative background risk to the model and translate the multiplicative risk vulnerability introduced by Franke et al.[2] into Mean-Variance framework.For the newsvendor problem with the multiplicative background risk, we obtain a set of reasonable conditions under which the newsvendor acts in a more cautious manner. Finally, we explore the effects of the first-order stochastic dominance and the mean-preservingrisk-spread shift in the two background risks on the optimal order quantity under suchcircumstances.