Risk Measures for DC Pension Plan Decumulation

ArXiv ID: 2502.16364 “View on arXiv”

Authors: Unknown

Abstract

As the developed world replaces Defined Benefit (DB) pension plans with Defined Contribution (DC) plans, there is a need to develop decumulation strategies for DC plan holders. Optimal decumulation can be viewed as a problem in optimal stochastic control. Formulation as a control problem requires specification of an objective function, which in turn requires a definition of reward and risk. An intuitive specification of reward is the total withdrawals over the retirement period. Most retirees view risk as the possibility of running out of savings. This paper investigates several possible left tail risk measures, in conjunction with DC plan decumulation. The risk measures studied include (i) expected shortfall (ii) linear shortfall and (iii) probability of shortfall. We establish that, under certain assumptions, the set of optimal controls associated with all expected reward and expected shortfall Pareto efficient frontier curves is identical to the set of optimal controls for all expected reward and linear shortfall Pareto efficient frontier curves. Optimal efficient frontiers are determined computationally for each risk measure, based on a parametric market model. Robustness of these strategies is determined by testing the strategies out-of-sample using block bootstrapping of historical data.

Keywords: Defined Contribution (DC) Plans, Decumulation Strategies, Stochastic Control, Left Tail Risk Measures, Financial Retirement Planning

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper uses advanced stochastic control theory and establishes theoretical equivalence between risk measures, indicating high mathematical density. It also employs computational methods, parametric model calibration, and out-of-sample testing with block bootstrapping on historical data, demonstrating significant empirical and implementation effort.

  flowchart TD
    A["Research Goal<br>Develop optimal DC plan<br>decumulation strategies"] --> B["Formulate Stochastic Control Problem<br>Define Reward: Total Withdrawals<br>Define Risk: Left Tail Measures"]
    B --> C{"Define Risk Measures"}
    C --> C1["Expected Shortfall"]
    C --> C2["Linear Shortfall"]
    C --> C3["Probability of Shortfall"]
    C1 & C2 & C3 --> D["Compute Efficient Frontiers<br>via Stochastic Control<br>using Parametric Market Model"]
    D --> E["Key Findings<br>1. Optimal controls for ES & LS<br>are identical<br>2. Out-of-sample robustness<br>verified via Bootstrapping"]