Securing Financial Comfort at Retirement An Analysis of Guaranteed Lifetime Withdrawal Benefit Contracts

Abstract

This thesis uses a backwards dynamic programming algorithm in conjunction with Monte Carlo simulation methods to determine optimal policyholder behavior facing a Variable Annuity contract with a Guaranteed Lifetime Withdrawal Benefit (GLWB) rider. The results show that an optimal policyholder facing a GLWB contract with Death Benefits is more likely to surrender a contract with the passage of time until reaching what this thesis defines to be the contract’s “critical point,” at and past which the policyholder would never surrender. This optimal behavior is used to determine the expected discounted future cash flows facing an optimal policyholder, which equate to the value of the contract. Sensitivity analysis of contract valuation is performed to better understand the influences of various contract assumptions on results. This thesis finds that the variables that most impact GLWB contract valuation are initial premium, guaranteed benefit payment amount, risk-free rate, and retirement age. Because such valuation is computationally time consuming, this thesis also presents a contract estimation method by making some simplifying assumptions and using Maximum Likelihood Estimation techniques and an l\(_{2}\) loss function.