Economic agents are exposed to the uncertain outcomes of future events. By enabling the exchange of securities, financial markets allow agents to reallocate their exposures in more efficient and mutually convenient arrangements to reduce perceived risks. The complexity and changing nature of the...

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...