Robust reward–risk ratio optimization with application in allocation of generation asset

Abstract

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.

Keywords:

• reward–risk measure
• performance ratio
• min-max optimization
• CVaR measure
• allocation of generation asset

Acknowledgements

This work is supported by Natural Science Foundation of China (10871031, 11171095) and the construct program of the key discipline in Hunan province, the Natural Science united Foundation of Hunan-Hengyang (10JJ8008) and the research project of Education Department of Hunan (10A015), the Research Grants Council under Grant (HKU7180/08E).