Optimal Portfolio with Ratio Type Periodic Evaluation under Short-Selling Prohibition

ArXiv ID: 2311.12517 “View on arXiv”

Authors: Unknown

Abstract

This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our goal is to understand the impact of the periodic reward structure on the long-run constrained portfolio strategy. For power and logarithmic utilities, we can reformulate the original problem into an auxiliary one-period optimization problem. To cope with the auxiliary problem with no short-selling, the dual control problem is introduced and studied, which gives the characterization of the candidate optimal portfolio within one period. With the help of the results from the auxiliary problem, the value function and the optimal constrained portfolio for the original problem with periodic evaluation can be derived and verified, allowing us to discuss some financial implications under the new performance paradigm.

Keywords: Utility Maximization, Portfolio Strategy, Constraint Optimization, Infinite Horizon, Performance Evaluation

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic control, duality theory, and fixed point analysis, evidenced by dense mathematical derivations and proofs in the excerpt, but it lacks any mention of backtests, datasets, or implementation details, focusing purely on theoretical characterization and numerical illustrations.

  flowchart TD
    A["Research Goal<br>Periodic Ratio Evaluation<br>No Short-Selling"] --> B["Problem Reformulation"]
    B --> C{"Utility Function"}
    C -->|Power/Log| D["Auxiliary One-Period Problem"]
    C -->|Other| E["Direct Solution Path"]
    D --> F["Dual Control Problem<br>Proxy for No-Shorting"]
    F --> G["Optimal Portfolio Characterization<br>One-Period Constraint"]
    G --> H["Original Problem Solution<br>Infinite Horizon Value Function"]
    H --> I["Key Findings<br>Periodic Reward Impact<br>Optimal Constrained Strategy"]
    E --> I