BFS 2002 

Contributed Talk 
Claudia Kluppelberg
We investigate some portfolio problems consisting of maximizing the expected terminal wealth under the constraint of an upper bound for the risk, where we measure risk by the variance, but also by the CapitalatRisk (CaR). The solution of the meanvariance problem has the same structure for any price process which follows an exponential Lévy process. The meanCaR involves a quantile of the corresponding wealth process of the portfolio. We derive a weak limit law for its approximation by a simpler Lévy process, often the sum of a drift term, a Brownian motion and a compound Poisson process. Certain relations between a Lévy process and its stochastic exponential are investigated.