Retirement Annuities: Optimization, Analysis and Machine Learning

Over the last few decades, we have seen a steady shift away from Defined Benefit (DB) pension plans to Defined Contribution (DC) pension plans in the United States. Even though a deferred income annuity (DIA) purchased while saving for retirement can pay aguaranteed stream of income for life, practically serving as a pension substitute, several questions arise. Our main contribution is answering the question of purchasing DIAs under the interest rate uncertainty. We pose the question as an optimal control problem, solve its centerpiece Hamilton-Jacobi-Bellman equation numerically, and provide a verification theorem. The result is an optimal DIA purchasing map.

With Cash Refund Income Annuities (CRIA) gaining traction quickly over the past few years, the literature is growing in the area of price sensitivity and its viability when viewed through the lens of key pricing parameters, particularly insurance loading. To that end, we explored the effect of reserving requirements on pricing and have analytically proven that, if accounted for properly at the beginning, reserving requirements would be satisfied at any time during the lifetime of the annuity.

Lower interest rates in the last decade prompted the explosion of fixed indexed annuities (FIAs) in the United States. These popular insurance policies offered a growth component with the addition of a lifetime income provisions. In FIAs, accumulation is achieved through exposure to a variety of indices while offering principal protection guarantees. The vast array of new products and features have created the need for a means of consistent comparisons between FIA products available to consumers. We illustr ate that statistical issues in the temporal and cross-sectional return correlations of indices used in FIAs necessitates more sophisticated modelling than is currently employed. We outline few novel approaches to handle these two issues. We model the risk control mechanisms of a class of FIA indices using machine learning. This is done using a small set of core macroeconomic variables as modelling features. This makes for more robust cross-sectional comparisons. Then we outline the properties of a sufficient model for said features, namely ‘rough’ stochastic volatility.