混合条件风险价值的随机单调性及其在库存系统中的应用  

Stochastic Monotonicity of Mixture Conditional Value-at-risk and Its Applications to Inventory System

作　　者：禹海波[1] 

机构地区：[1]北京工业大学经济与管理学院,北京100124

出　　处：《应用数学学报》2014年第5期805-823,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(NO.70971001)资助项目

摘　　要：运用应用概率中的随机占优和可变序研究一类与前景理论中损失规避有关的混合条件风险价值的随机单调性及其在库存管理中的应用.引入用于刻画决策者损失规避和风险偏好特性的风险偏好系数λ,得到混合条件风险价值关于此风险偏好系数和风险水平η的单调性和上下界.证明对大于或等于1的风险偏好系数,混合条件风险价值在一阶和二阶随机占优意义下具有随机单调性;对小于1的风险偏好系数,混合条件风险价值在凸序意义下具有随机单调性.从实际应用方面考虑混合条件风险价值约束库存系统,得到系统最优订货量和最优利润关于风险偏好系数的单调性及其上下界.证明对大于或等于1的风险偏好系数,系统最优利润在一阶和二阶随机占优意义下具有随机单调性;然而,当风险偏好系数足够小(如取0)时,此结论不一定成立.我们通过数值例子验证:当风险偏好系数足够小(如取0)且风险水平η足够大(如取值大于0.5)时系统最优利润随需求可变性的增加而增加,这与风险中性和风险规避情形的结果不相同.We analyze stochastic monotonicity of mixture conditional value-at-risk （CVaR） with respect to loss aversion within Prospect Theory and its applications to inventory system by using stochastic dominance and variability orderings in applied probability. We introduce a measure λ, called risk preference coefficient, describing loss aversion and risk preference of decision maker, and monotonicities of the mixture CVaR with respect to risk preference coefficient and risk level η and upper and lower bounds are obtained. We prove that mixture- CVaR has monotonicity under the first and second degree stochastic dominance for any risk preference coefficient which is larger than or equal to one; it has monotonicity under the convex ordering for those risk preference coefficients which are strictly smaller than one. From the perspective of practical application, we consider a inventory system with mixture- CVaR constrain, and the monotonicities of the optimal order quantity and profit with respect to risk preference coefficient and upper and lower bound are obtained. We show that optimal profit has monotonicity under the first and second degree stochastic dominance for any risk preference coefficient which is larger than or equal to one; however, this maybe not true for those risk preference coefficients which is smaller enough （such as taking zero）. Numerical example states clearly that if the risk preference coefficient is enough smaller （such as taking zero） and risk level r/is enough larger （such as taking value larger than 0.5）, then the optimal profit will increase as demand variability increases.

关 键 词：混合条件风险价值 损失规避 风险偏好 可变性 随机单调性 

分 类 号：O224[理学—运筹学与控制论] O227[理学—数学]