Conditional value-at-risk approach and its optimization of newsvendor with risk preference

Newsvendor's profit distribution function is developed, and the formula of value-at-risk(VaR) is derived directly at a giving risk level. Conditional VaR(CVaR) models with different order quantity and risk levels are developed respectively for risk-averse and risk-taking with considering of shortage cost. The integration variable in the models is changed to random demand instead of profit, which makes it easy to solve CVaR model with VaR. The optimal decision of newsvendor with CVaR is studied under giving risk level. On this basis, the CVaR model and optimal decision are also discussed with no shortage cost. The expected profit and optimal decision of risk-neutral newsvendor can be derived from the related formula of risk-averse or risk-taking. Finally, the study directions are indicated.