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Minimum return guarantees, investment caps, and investment flexibility

We study the merits of capped retirement products with guarantee for investors who have the flexibility to dynamically adjust their investment strategy. All contracts under consideration are fairly priced such that the net profit of the provider is zero. Without the rider, an expected utility maximizing CRRA investor does not want an investment cap. Here, she commits herself to a strategy a priori. With the flexibility rider, the optimization problem changes and the optimal strategy is a response to an exogenously set price. A fair pricing then anticipates the optimal response of the investor. We show that the maximum expected utility of the investor can, for anticipated fairly priced products, be obtained for a finite cap. Thus, a capped product design can give a Pareto improvement to the otherwise uncapped contract version.