Paper: arXiv 2410.20060

Abstract

This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption level, death benefit, and terminal wealth. Meanwhile, the individual faces a convex-set trading constraint, of which the non-tradeable asset constraint, no short-selling constraint, and no borrowing constraint are special cases. Following Cuoco (1997), we build the artificial markets to derive the dual problem and prove the existence of the original problem. With additional discussions, we extend his uniformly bounded assumption on the interest rate to an almost surely finite expectation condition and enlarge his uniformly bounded assumption on the income process to a bounded expectation condition. Moreover, we propose a dual control neural network approach to compute tight lower and upper bounds for the original problem, which can be utilized in more general cases than the simulation of artificial markets strategies (SAMS) approach in Bick et al. (2013). Finally, we conclude that when considering the trading constraints, the individual will reduce his or her demand for life insurance.

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper uses advanced mathematical techniques like dual control, artificial markets, and rigorous proofs of existence under weak assumptions, but the empirical validation is purely theoretical simulation (neural network on synthetic data) without real backtests or live data.

Research Flowchart

  flowchart TD
  A["Research Goal: Constrained Portfolio Optimization in a Life-Cycle Model"] --> B["Methodology: Dual Control via Artificial Markets"]
  B --> C["Input: Stochastic Income & Asset Processes"]
  C --> D{"Computation: Dual Control Neural Network"}
  D -->|Training| E["Tight Lower & Upper Bounds"]
  E --> F["Key Findings: Trading Constraints Reduce Life Insurance Demand"]