The recent crisis made it evident that replicating the performance of a benchmark is not a sufficient goal to meet the expectations of usually risk-averse investors. The manager should also consider that the investor are seeking for a downside protection when the benchmark performs poorly and...

In this contribution we propose a dynamic tracking error problem and we consider the problem of monitoring at discrete point the shortfall of the portfolio below a set of given reference levels of wealth. We formulate and solve the resulting dynamic optimization problem using stochastic...