Pricing arithmetic Asian and Amerasian options: A diffusion operator integral expansion approach

In this paper, we propose a new explicit series expansion formula for the price of an arithmetic Asian option under the Black–Scholes model and Merton's jump-diffusion model. The method is based on an equivalence in law relation together with the diffusion operator integral method proposed by Heath and Platen. The method yields explicit series expansion formula for the Asian options' prices. The theoretical convergence of the expansion to the true value is established. We also consider the American Asian option (i.e., Amerasian option) and derive the corresponding expansion formula through the early exercise premium representation. Numerical results illustrate the accuracy and efficiency of the method as compared with benchmarks in the literature.     

自拟中药方剂养胃汤加减治疗慢性萎缩性胃炎患者的疗效

目的探讨自拟中药方剂养胃汤加减治疗慢性萎缩性胃炎患者的疗效。方法选取2018年11月至2019年11月营口市中医院收治的100例慢性萎缩性胃炎患者作为研究对象,随机分为胃复春片组与联合用药组,各50例。胃复春片组给予胃复春片,联合用药组在对照组治疗基础上采用自拟中药方剂养胃汤加减治疗,比较两组中医证候积分,炎症介质及胃泌素-17(G-17)、胃蛋白酶原Ⅰ(PGⅠ)、胃蛋白酶原Ⅱ(PGⅡ)水平,一氧化氮(NO)、超氧化物歧化酶(SOD)、丙二醛(MDA)水平及不良反应。结果治疗后联合用药组胃刺痛、胃脘胀满、食少纳呆、消瘦及乏力积分低于胃复春片组(P<0.05);治疗后,联合用药组CRP、TNF-α及IL-6水平低于胃复春片组(P<0.05),G-17、PGⅠ、PGⅡ高于胃复春片组(P<0.05);治疗后,联合用药组NO、SOD水平高于胃复春片组(P<0.05),MDA水平低于胃复春片组(P<0.05);两组不良反应发生率比较,差异无统计学意义(P>0.05)。结论自拟中药方剂养胃汤加减治疗慢性萎缩性胃炎能有效缓解患者症状,减轻机体炎症反应,未增加不良反应发生率。     

Energy storage strategy analysis based on the Choquet multi-criteria preference aggregation model: The Portuguese case

With the increase in renewable energy generation and its problems related to output instability, storage systems must be implemented in parallel to account for this effect. Therefore, it is valuable to deepen the study of these technologies’ performances in their several application tiers, thus understanding the potential of each alternative, both per tier and as a whole. For this reason, a collaborative multi-criteria decision-aiding framework is proposed to rank the various available options in several layers of the energy storage market, constructed alongside experts and policy-makers from each tier that serve as actors of the decision-making process and using Portugal as a case study. Based on the Choquet multi-criteria preference aggregation model, to the best of the authors’ knowledge, this framework is an unprecedented application in the energy sector. Beyond a critical review of the results, a scenario analysis was performed to explore interesting future possibilities that may aid governments to make decisions in the search for an energy sustainable development. Chemical storage solutions, such as Hydrogen and Methane, as well as several electrochemical batteries, especially Lithium- and Nickel-based ones, were the standout energy storage solutions. Chemical storage was shown to have the desired characteristics for the Long-term grid tier. Meanwhile, batteries, including Redox Flow in the first case, have overperformed in the Microgrid and Mobility tiers. No standout solutions appeared in the Short-term grid tier. Unsurprisingly, the aforementioned chemical storage systems, batteries, and Hot Water have presented themselves as the most politically interesting technologies, due to their multipurpose uses and intrinsic characteristics.