Mean-variance trading portfolio selection for a class of energy retailers

Due to the volatile price of various energy products, energy retailers in many countries are facing the risk of going bankrupt. This paper focuses on a class of energy retailers that trade energy products including the electricity option, the natural gas option and the white certificate. From the perspective of such energy retailers, this paper studies a portfolio selection strategy that can achieve the maximized asset value and mitigate the potential risk of purchasing energy products at high prices. Firstly, a class of linear ordinary differential equations (ODEs) and stochastic differential equations (SDEs) are used to model the dynamic time-varying price of electricity option, natural gas option and white certificate accurately. Secondly, based on the mean-variance model, the portfolio selection strategy problem of energy retailers trading these three products is formulated as a stochastic optimal control problem. Then, the linear-quadratic (LQ) control method is used to solve the problem analytically with mathematical theorem, and the obtain controller is indeed the desired optimal trading strategy. Finally, a series of examples demonstrating the correctness of the proposed portfolio selection strategy are provided.