BFS 2002

Contributed Talk

Optimal portfolios with bounded Capital-at-Risk

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 Capital-at-Risk (CaR). The solution of the mean-variance problem has the same structure for any price process which follows an exponential LÚvy process. The mean-CaR involves a quantile of the corresponding wealth process of the portfolio. We derive a weak limit law for its approximation by a simpler LÚvy process, often the sum of a drift term, a Brownian motion and a compound Poisson process. Certain relations between a LÚvy process and its stochastic exponential are investigated.