The Mean-CVaR Portfolio Selection With Background Risk

In this paper, we study the portfolio selection with background risk in mean-CVaR framework. As a benchmark model, we firstly give out the portfolio frontier and the minimum variance portfolio with background risk in mean-variance setting. Secondly, we replace variance with conditional value at risk(CVaR) as a measure of risk, and this paper explores the portfolio frontier in mean-CVaR framework with background risk. We present the portfolio frontier and the minimum CVaR portfolio with background risk. Then, we specify the relation between mean-CVaR and mean-variance portfolio. Finally, we take the transaction costs into account in mean-CVaR environment. In addition, we propose several numerical examples to explain our results at the end of each section.