Paper: arXiv 2309.01936

Abstract

This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension member. The member’s aim is to maximize the expected utility from the terminal wealth exceeding the minimum guarantee by investing his wealth in a cash bond, an inflation-linked bond and a stock. Due to the presence of the tail VaR constraint, the problem cannot be tackled by standard control tools. We apply the Lagrange method along with quantile optimization techniques to solve the problem. Through delicate analysis, the optimal investment output in closed-form and optimal investment strategy are derived. A numerical analysis is also provided to show how the constraints impact the optimal investment output and strategy.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced stochastic calculus, martingale methods, and quantile optimization to derive closed-form solutions for a complex optimal investment problem under tail VaR and portfolio insurance constraints. While it includes a numerical analysis, the absence of real data, backtests, or implementation details places it firmly in theoretical research.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Optimal DC Pension Management<br>under Tail VaR & Inflation Risk"] --> B["Key Methodology:<br>Lagrange Method &<br>Quantile Optimization"]
  B --> C["Data/Inputs:<br>Stock, Cash Bond,<br>Inflation-Linked Bond"]
  C --> D["Computational Process:<br>Transforming Tail VaR Constraint<br>into Solvable Optimization"]
  D --> E{"Outcomes"}
  E --> F["Closed-form<br>Optimal Investment Output"]
  E --> G["Analytical<br>Optimal Investment Strategy"]
  E --> H["Numerical Analysis<br>showing impact of constraints"]