Research On Three Decision Problems Based On The CVaR Risk Measure

This article is mainly composed of three parts:(1) Under the assumption of the rates of return of the risk assets with a multivariate normal distribution, we explore the portfolio selection problem with a singular variance-covariance matrix under the mean-CVaR criterion. we find out the specific form of portfolio selection under the general market condition. (2) When random demand is dependent on the shelf space, we study the retailer’s optimal ordering decision under the two expected demand form based on CVaR risk measure. Further, We show the change of expected revenue about system parameters through the numerical analysis. (3) In a Conditional Value-at-Risk framework, this paper deals with a risk-averse newsvendor model under the assumption that the random demand is price and shelf-space sensitive. An analytical solution is provided for finding the optimal selling price and shelf-space. The influences of system parameters on the optimal decisions are investigated as well. Numerical examples illustrate how the optimal expected revenue changes with the system parameters.