Similar to the EUT and CPT case, for all contracts the certainty equivalent return increases with increasing [theta], the optimal value of [theta] is 1, and the constant mix strategy dominates the other contracts.
These outcomes get overweighted and generate a higher certainty equivalent return. The constant mix contract also contains high gains that happen with low probabilities, but also high losses that happen with low probabilities, which reduce the certainty equivalent return.
Here, the MCPT certainty equivalent return of the more complex guaranteed products (ratch-up and cliquet) exceeds the roll-up and the constant mix contract.
Therefore, the MCPT certainty equivalent return difference between the constant mix and the guaranteed contracts is even larger in this case.
For each fixed level of [alpha], the cliquet contract generates the highest certainty equivalent return. The overall maximum certainty equivalent return for the cliquet and therefore for all contracts is 4.79 percent for [alpha] = 0.6 and [theta] [approximately equal to] 0.5.
the cliquet contract for s = 0.5 generate the highest combined certainty equivalent return. Similar results can be seen in the upper panels for the case [alpha] = 0.6.