Portfolio insurance under a risk-measure constraint

► We study a portfolio insurance where a fund manager guarantees that the portfolio value will be above a threshold. ► The fund manager pays an initial fee to the bank which refunds, when it is needed, the investor. ► In exchange for this protection, the bank imposes a limit on the risk exposure of the fund manager. ► We give a full solution to this problem. Explicit results are provided for the entropic and spectral risk measures.