Paper: arXiv 2303.08462

Authors: Kenneth Tsz Hin Ng, Wing Fung Chong

Abstract

Optimal investment strategies of an individual worker during the accumulation phase in the defined contribution pension scheme have been well studied in the literature. Most of them adopted the classical backward model and approach, but any pre-specifications of retirement time, preferences, and market environment models do not often hold in such a prolonged horizon of the pension scheme. Pre-commitment to ensure the time-consistency of an optimal investment strategy derived from the backward model and approach leads the supposedly optimal strategy to be sub-optimal in the actual realizations. This paper revisits the optimal investment problem for the worker during the accumulation phase in the defined contribution pension scheme, via the forward preferences, in which an environment-adapting strategy is able to hold optimality and time-consistency together. Stochastic partial differential equation representation for the worker’s forward preferences is illustrated. This paper constructs two of the forward utility preferences and solves the corresponding optimal investment strategies, in the cases of initial power and exponential utility functions.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework using Stochastic Partial Differential Equations (SPDEs) and forward utility theory to solve long-horizon pension investment problems. While mathematically rigorous and novel in addressing time-inconsistency without pre-commitment, it lacks empirical backtesting, real market data validation, or implementation code.

Research Flowchart

  flowchart TD
    A[Research Goal: Time-Consistent Optimal Investment in DC Pension via Forward Utility] --> B[Inputs: Initial Power & Exponential Utility + Market Stochastic Dynamics]
    B --> C[Methodology: Formulate Forward Utility via Stochastic PDEs]
    C --> D[Compute Optimal Investment Strategies & Solve SPDEs]
    D --> E[Outcome: Environment-Adapting Strategies Maintaining Optimality over Long Horizons]