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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.
The stochastic monotonicity of the VaR associated with the loss avoidance in the foreground theory and its application to inventory management are studied by using the stochastic dominance and the variable order in the applied probabilities. Preference characteristics of the risk preference coefficient λ to get the mixed conditions risk value on the risk preference coefficient and risk level η monotonicity and upper and lower bounds prove that the risk preference greater than or equal to 1 coefficient of mixed risk value in the first and second order Random preference is random monotonicity. For the risk preference coefficient less than 1, the mixed condition risk value is stochastically monotonic in the convex order. From the practical application, we consider the mixed condition risk value constrained inventory system to obtain the optimal system order The monotonicity and its upper and lower bounds of the risk preference coefficients of the quantity and the optimal profit prove that for the risk preference coefficient greater than or equal to 1, the system optimal profit has a random monotonicity in the first and second order stochastic dominance; however, When the risk preference coefficient is small enough (such as taking 0), this conclusion may not be true.We verify the numerical example: when the risk preference When the number is small enough (eg 0) and the risk level η is large enough (eg, the value is greater than 0.5), the optimal profit of the system increases with the increase of demand variability, which is different from the result of risk neutrality and risk avoidance.