“报童问题”中风险偏好下的条件风险值及其优化

建立了报童随机利润的分布函数，得到任意风险水平下的VaR解析表达式或应满足的条件。考虑缺货成本，针对风险规避和风险偏爱两种情况，分别建立不同订购量和风险水平下的条件风险值模型，并将模型中对利润变量的积分转换为对随机需求变量的积分，解决了模型中因包含VaR变量而求解困难的问题。分析了给定风险水平下的最优决策，讨论了缺货成本为0的特殊情形。风险中性报童的期望利润与最优决策可由风险规避或风险偏爱的相应公式推导。最后对下一步的研究方向进行了展望。

Conditional value-at-risk approach and its optimization of newsvendor#br# 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.