Paper: arXiv 2611.06495

Authors: Yueman Feng, Wenyuan Li

Abstract

This paper studies constrained defined contribution (DC) pension management under a two-factor financial market model. The pension participant is allowed to invest in cash, two nominal bonds, an inflation-linked bond, and a stock index. Moreover, they can also purchase term life insurance to manage pre-retirement death risk. Unlike traditional literature, we consider a pension member restricted to a general non-empty, closed, and convex trading constraint set that includes no short-selling, no borrowing, and portfolio-mix constraints as special cases. Such restrictions reflect common limits on pension-account trading. To solve the problem, we construct a family of unconstrained artificial markets, in which the original trading constraints are satisfied by adjusting the drift terms of the risky assets. Using a duality transformation, we derive the Lagrangian dual problem and propose a reparameterized neural network method to compute lower and upper bounds on the primal value function. We calibrate our model with U.S. data using a Kalman filter method, and find that our method produces a smaller duality gap than the benchmark methods. We also compare the constrained results with the unconstrained explicit solution and find that trading constraints substantially change wealth accumulation, portfolio strategies, and insurance demand. This highlights that unconstrained solutions may provide misleading guidance for pension management in practice.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly complex mathematical framework for constrained pension management, employing advanced techniques like duality transformation and reparameterized neural networks. It demonstrates strong empirical rigor through model calibration with U.S. data and comparison with benchmark methods, showing a significant reduction in duality gap. The novelty lies in addressing general convex trading constraints within a two-factor market model and integrating life insurance, offering a more realistic and robust solution than prior literature.

Research Flowchart

  flowchart TD
    A[Research Goal: Constrained DC Pension Management under Two-Factor Model] --> B{Key Methodology: Reparameterized Neural Network for Constrained Optimization};
    B --> C[Problem Formulation: General Non-empty, Closed, Convex Trading Constraint Set];
    C --> D[Data/Inputs: U.S. Market Data Calibrated via Kalman Filter];
    D --> E[Computational Process: Solve Lagrangian Dual Problem to Compute Bounds];
    E --> F[Key Finding 1: Smaller Duality Gap than Benchmark Methods];
    F --> G[Key Finding 2: Constraints Substantially Alter Wealth, Portfolio, Insurance Demand];
    G --> H[Outcome: Unconstrained Solutions Misleading for Practical Pension Management];