A novel energy management system to improve the efficiency of renewable energy and storage system by scheduling various types of household appliances is developed. The end users schedule appliances optimally taking into account maximum utility (a measure of the satisfaction level of user’s electricity consumption) as well as minimum user’s cost of energy as competitive objectives. A random disturbance (reflecting an uncertainty) is introduced to describe the indeterminate amount of the electricity produced from the renewable energy sources at the adjacent slots. By applying the probability theory, the uncertain optimization model is transformed into a convex optimization problem. Then, the optimal solution is obtained using a quasi-Newton method. The rationality of our proposed model is verified through numerical simulations. According to the results of simulation studies, it is demonstrated that our proposed model not only enhances users’ utility but also reduces energy consumption cost.

In this paper, we consider the nonergodic Ornstein-Uhlenbeck processdriven by the weighted fractional Brownian motion B a,b t with parameter a and b. Our goal is to estimate the unknown parameter θ > 0 based on the discrete observations of the process. We construct two estimatorsθ n andθ n of θ and show their strong consistency and the rate consistency.

In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption; cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility, and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal; they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.

A new framework for pricing European vulnerable options is developed in the case where the underlying stock price and firm value follow the mixed fractional Brownian motion with jumps, respectively. This research uses the actuarial approach to study the pricing problem of European vulnerable options. An analytic closed-form pricing formula for vulnerable options with jumps is obtained. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in the paper. Finally, we compare and analyze the pricing results of different pricing models and discuss the influences of basic parameters on the pricing results of our proposed model by using numerical simulations, and the corresponding economic analyses about these influences are given.