Verification Theorems for Models of Optimal Consumption and Investment with Retirement and Constrained Borrowing

Verification Theorems for Models of Optimal Consumption and Investment with Retirement and Constrained Borrowing

0.00 Avg rating0 Votes
Article ID: iaor201111565
Volume: 36
Issue: 4
Start Page Number: 620
End Page Number: 635
Publication Date: Nov 2011
Journal: Mathematics of Operations Research
Authors: ,
Keywords: programming: dynamic, economics
Abstract:

Proving verification theorems can be tricky for models with both optimal stopping and state constraints. We pose and solve two alternative models of optimal consumption and investment with an optimal retirement date (optimal stopping) and various wealth constraints (state constraints). The solutions are parametric in closed form up to at most a constant. We prove the verification theorem for the main case with a nonnegative wealth constraint by combining the dynamic programming and Slater condition approaches. One unique feature of the proof is the application of the comparison principle to the differential equation solved by the proposed value function. In addition, we also obtain analytical comparative statics.

Reviews

Required fields are marked *. Your email address will not be published.