Optimal Portfolios with Guarantee at Maturity : Computation and Comparison

Portfolio insurance allows investors to recover, at maturity, a given percentage of their initial capital. This limits downside risk in falling markets. Besides, it allows some participation in rising markets. One of the standard portfolio insurance methods is the Constant Proportion Portfolio Insurance (CPPI). We analyse options on cushion associated to CPPI. This kind of Power options corresponds in particular to the solution of a portfolio optimization problem in which an additional guarantee constraint must be satisfied at maturity. We also compare this strategy with the standard OBPI method