General-Utility Analysis of Exponentially Growing Guarantees

Establish a solution theory for the retirement planning control problem with exponentially growing minimum benefit and wealth floors under general utility functions, extending the CRRA analysis developed in Appendix Section “Exponentially Growing Guarantees.”

Background

The paper studies retirement planning with minimum guarantees on both the benefit rate and fund wealth. In Appendix Section “Exponentially Growing Guarantees,” the authors show that, under CRRA utility, deterministic floors of the form b(t) ≥ b₀e^{νt} and X(t) ≥ αx₀e^{νt} can be transformed into a time-homogeneous problem with modified parameters. The conclusion explicitly identifies the corresponding extension to general utility functions as unresolved.