We characterize the investor’s optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. The set of feasible portfolios might no longer be connected or convex, while the number of local optima...

An intensive and still growing body of research focuses on estimating a portfolio’s Value-at-Risk. Depending on both the degree of non-linearity of the instruments comprised in the portfolio and the willingness to make restrictive assumptions on the underlying statistical distributions, a...