Economy and Management Science
Over past decades, deceptive counterfeits which cannot be recognized by ordinary consumers when purchasing, such as counterfeit cosmetics, have posed serious threats on consumers’ health and safety, and resulted in huge economic loss and inestimable brand damages to the genuine goods at the same time. Thus, how to effectively control and eliminate deceptive counterfeits in the market has become a critical problem to the local government. One of the principal challenges in combating the cheating action for the government is how to enhance the enforcement of relative quality inspection agencies like industrial administration office (IAO). In this paper,we formulate a two-stage counterfeit product model with a fixed checking rate from IAO and a penalty for holding counterfeits. Tominimize the total expected cost over two stages,the retailer adopts optimal ordering policies which are correlated with the checking rate and penalty. Under certain circumstances, we find that the optimal expected cost function for the retailer is first-order continuous and convex. The optimal ordering policy in stage two depends closely on the inventory level after the first sales period. When the checking rate in stage one falls into a certain range, the optimal ordering policy for the retailer at each stage is to order both kinds of products. Knowing the retailer’s optimal ordering policy at each stage, IAO can modify the checking rate accordingly to keep the ratio of deceptive counterfeits on the market under a certain level.
Bond portfolio immunization is a classical issue in finance. Since Macaulay gave the concept of duration in 1938, many scholars proposed different kinds of duration immunization models. In the literature of bond portfolio immunization using multifactor model, to the best of our knowledge, researchers only use the first-order immunization, which is usually called as duration immunization, and no one has considered second-order effects in immunization, which is well known as “convexity” in the case of single-factor model. In this paper, we introduce the second-order information associated with multifactor model into bond portfolio immunization and reformulate the corresponding problems as tractable semidefinite programs. Both simulation analysis and empirical study show that the second-order immunization strategies exhibit more accurate approximation to the value change of bonds and thus result in better immunization performance.
In this paper, we propose an inexact proximal point method to solve equilibrium problems using proximal distances and the diagonal subdifferential. Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction, we prove that the sequence generated by the method converges to a solution point of the problem.
