In this article, we study reward–risk ratio models under partially known message of random variables, which is called robust (worst-case) performance ratio problem. Based on the positive homogenous and concave/convex measures of reward and risk, respectively, the new robust ratio model is reduced equivalently to convex optimization problems with a min–max optimization framework. Under some specially partial distribution situation, the convex optimization problem is converted into simple framework involving the expectation reward measure and conditional value-at-risk measure. Compared with the existing reward–risk portfolio research, the proposed ratio model has two characteristics. First, the addressed problem combines with two different aspects. One is to consider an incomplete information case in real-life uncertainty. The other is to focus on the performance ratio optimization problem, which can realize the best balance between the reward and risk. Second, the complicated optimization model is transferred into a simple convex optimization problem by the optimal dual theorem. This indeed improves the usability of models. The generation asset allocation in power systems is presented to validate the new models. 相似文献
Experiments designed to prepare Ziegler‐Natta catalysts with controlled particle morphology are reported. Different dealcoholation processes are used on the adduct MgCl2 · nEtOH to prepare the catalysts: either thermal treatment or chemical dealcoholation employing different substances such as titanium tetrachloride, triethylaluminium, dichlorodimethylsilane, and chlorotrimethylsilane. In addition, dichlorodimethylsilane dealcoholation is also performed after thermal treatment. SEM analysis of adducts, supports, and catalysts is carried out. The obtained catalysts are characterized through impregnated titanium content evaluation. The polyethylenes and poly(propylene)s obtained employing the so prepared catalysts show spherical morphology when examined by optical microscopy.