Verification theorems for models of optimal consumption and investment with annuitization

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 analytic comparative statics for the optimal consumption and investment strategies with annuitization. •I prove the uniqueness and existence theorem for models of optimal consumption and investment with annuitization.•I apply the variational inequality approach of Bensoussan and Lions (1982).•I obtain analytic comparative statics for the optimal strategies.