Title: Static and Dynamic VaR Consrained Portfolios with Application to Delegated Portfolio Management
Authors: Mustafa C. Pinar

We give a closed-form solution to the single-period portfolio selection problem with a Value-at-Risk (VaR) constraint in the presence of a set of risky assets with multivariate normally distributed returns and the risk-less account without short sales restrictions. The result allows to obtain a very simple, myopic dynamic portfolio policy in the multiple period version of the problem. We also consider mean-variance portfolios under a probabilistic chance (VaR) constraint, and give an explicit solution. We use this solution to calculate explicitly the bonus of a portfolio manager to include a VaR constraint in his/her portfolio optimization, which we refer to as the price of a VaR constraint.
Keywords: Dynamic portfolio selection, probabilistic chance constraint, Value-at-Risk, mean-variance efficient portfolios, delegated portfolio management.