Narrow Results

A supply chain with a supplier and a risk-averse retailer is considered in the paper under trade credit contract. The retailer as newsvendor faces a non-negative random demand and the supplier provides the trade credit for the risk-averse retailer with budget constraints. Different from the existing research, in a conditional value-at-risk (CVaR) framework, the optimal ordering quantity and wholesale price are obtained. Analytical results are obtained for the newsvendor retailer’s optimal ordering quantity and supplier’s optimal wholesale price under CVaR measure. Sensitivity analysis is also yielded. It is found that the optimal ordering quantity decreases as the degree of risk aversion increases. Furthermore, we analyze the effect of the initial budget of retailer and the wholesale price on the order quantity decision. This paper also finds that the trade credit contract could create value for a risk-averse supply chain with budget constraints. Finally, to compare with the existing results the theoretical analysis and numerical examples are illustrated.

This paper investigates the coherent risk measure of a class of normal mixture distributions which are widely-used in finance. The main result shows that the mean-risk portfolio optimization problem with these normal mixture distributions can be reduced to a quadratic programming problem which has closed form of solution by fixing the location parameter and skewness parameter. In addition, we show that the efficient frontier of the portfolio optimization problem can be extended to three dimensions in this case. The worst-case value-at-risk in the robust portfolio optimization can also be calculated directly. Finally, the conditional value-at-risk (CVaR) is considered as an example of coherent risk measure. We obtain the marginal contribution to risk for a portfolio based on the normal mixture model.

Large-scale wind power may have a negative impact on peak regulation, frequency regulation and the security of power grid for its great randomness and intermittence. This paper proposes two indices VaR and CVaR to evaluate the risk and to provide dispatching operation decision-making. It demonstrates physical meaning and practical application of the two indices with wind power output of Northeast China Power Grid in 2015. Then, it analyzes the wind power output simultaneity index and the wind power output change rate in 5 minutes. Further, the paper evaluates the wind power effect on peak and frequency regulation with probabilistic methods.