Verification Theorems for Optimal Consumption and Investment Problems with Annuitization
Posted: 25 Feb 2016 Last revised: 13 Apr 2020
Date Written: November 17, 2017
Abstract
One can find it challenging to deal with verification theorems for optimal consumption and investment problems with annuitization. I pose a tractable framework to prove verification theorems for the problems. I revisit an annuitization model of Park (2015) and prove the verification theorem for the model. A key idea of the proof is the application of the variational inequality approach of Bensoussan and Lions (1982) to the annuitization problem solved by the suggested value function. Further, I obtain analytical comparative statics for the optimal consumption and investment strategies with annuitization.
Keywords: annuitization, existence, uniqueness, variational inequality
JEL Classification: G11, G12, J26
Suggested Citation: Suggested Citation