Optimal portfolio under ratio-type periodic evaluation in stochastic factor models under convex trading constraints

ArXiv ID: 2411.13579 “View on arXiv”

Authors: Unknown

Abstract

This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon, featuring the dynamic adjustments in portfolio decision according to past achievements. Under power utility, we transform the original infinite horizon optimal control problem into an auxiliary terminal wealth optimization problem under a modified utility function. To cope with the convex trading constraints, we further introduce an auxiliary unconstrained optimization problem in a modified market model and develop the martingale duality approach to establish the existence of the dual minimizer such that the optimal unconstrained wealth process can be obtained using the dual representation. With the help of the duality results in the auxiliary problems, the relationship between the constrained and unconstrained models as well as some fixed point arguments, we finally derive and verify the optimal constrained portfolio process in a periodic manner for the original problem over an infinite horizon.

Keywords: Utility Maximization, Portfolio Optimization, Martingale Duality, Stochastic Control, Periodic Utility, Multi-Asset

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper presents a highly theoretical, mathematical framework involving stochastic control, duality theory, and fixed-point arguments in infinite-horizon stochastic factor models, with no mention of backtesting, empirical data, or implementation details.
  flowchart TD
    A["Research Goal: Find Optimal Portfolio under Periodic Ratio Evaluation with Convex Constraints"] --> B["Methodology: Power Utility Transformation"]
    
    B --> C["Auxiliary Problem: Terminal Wealth Optimization with Modified Utility"]
    C --> D["Unconstrained Model: Martingale Duality Approach"]
    D --> E["Dual Minimizer & Optimal Wealth via Duality Representation"]
    E --> F["Constrained Model: Fixed Point Arguments & Duality Mapping"]
    
    F --> G["Key Outcome: Verified Optimal Constrained Portfolio Process"]
    G --> H["Periodic Adjustments Derived over Infinite Horizon"]