Three Essays in Life Cycle Modelling

Abstract

This thesis explores critical aspects of discrete-time life-cycle modeling, focusing on optimization techniques and decision-making strategies for retirement planning and portfolio management. It is composed of three essays, each addressing distinct but interrelated challenges in life-cycle financial models.

The first essay establishes a proof of monotonicity between pre-decision and post-decision state variables, with particular focus on the savings function, in the context of stochastic portfolio optimization using the Endogenous Gridpoint Method (EGM). Establishing this proof reinforces the theoretical validity of applying EGM in this setting and helps ensure that a key structural condition, namely monotonicity, is satisfied. This extends the method's applicability to a broader class of problems involving stochastic portfolio returns and addresses a gap in prior literature where this assumption was often left unverified.

The second essay investigates a life-cycle retirement planning problem, comparing four different investment strategies: Self-Management with Dynamic Investment, Self-Management with Benchmark Investment, Hire-Management with Flexible Allocation, and Hire-Management with Alpha Focus. Using dynamic programming techniques, this study optimizes investment allocation and consumption patterns during the Defined Contribution accumulation phase, leading to a life annuity purchase at retirement. The results show that while delegated investment options can enhance a worker's retirement outcome, higher fund fees in the US market and associated agency cost may limit their value.

The third essay explores the application of the Least-Squares Monte Carlo (LSMC) method to life-cycle utility-based models in retirement savings, a field where its use has been relatively limited. By comparing LSMC's computational efficiency and accuracy with traditional dynamic programming method (i.e., Value Function Iteration), the study highlights its potential to improve decision-making in post-retirement financial planning, particularly in optimizing investment, consumption, and annuitization strategies.

Together, these essays contribute to the literature on life-cycle financial planning by offering new insights into the mathematical and computational techniques that enhance decision-making for both individuals and financial institutions. Show more