Risk managers use portfolios to diversify away the unpriced risk of individual securities. In this article we compare the benefits of portfolio diversification for downside risk in case returns are normally distributed with the case of fat-tailed distributed returns. The downside risk of a...

The paper characterizes first and second order tail behavior ofconvolutions of i.i.d. heavy tailed random variables with supporton the real line. The result is applied to the problem of riskdiversification in portfolio analysis and to the estimation of theparameter in a MA(1) model.

Contemporary financial stochastic programs typically involve a trade-offbetween return and (downside)-risk. Using stochastic programming we characterize analytically (rather than numerically) the optimal decisions that follow from characteristic single-stage and multi-stage versions of such...

The stock market collapse led to political tensions between generations due to the fuzzy definition of the property rights over the pension funds’ wealth. The problem is best resolved by the introduction of generational accounts. Modern consumption and portfolio theory shows that the younger...

Portfolio risk is in an important way driven by 'abnormal' returns emanating from heavy tailed distributed asset returns. The theory of regular variation and extreme values provides a model for this feature of financial data. We first review this theory and subsequently study the problem of...

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...

We show that if an agent is uncertain about the precise form of his utility function, his actual relative risk aversion may depend on wealth even if he knows his utility function lies in the class of constant relative risk aversion (CRRA) utility functions. We illustrate the consequences of this...