Paper: arXiv 2411.13579

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]

Cited References (49)

  1. Portfolio Selection, Periodic Evaluations and Risk Taking (2023) — link
  2. Portfolio Optimization with Allocation Constraints and Stochastic Factor Market Dynamics — → 2303.09835
  3. An Optimal Consumption Problem for General Factor Models (2018) — link
  4. Borrowing constraints, effective flexibility in labor supply, and portfolio selection (2018) — link
  5. Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem (2018) — link
  6. PORTFOLIO OPTIMIZATION AND STOCHASTIC VOLATILITY ASYMPTOTICS (2017) — link
  7. The Real Effects of Short-Selling Constraints (2014) — link
  8. Strategic Asset Allocation (2013) — link
and 41 more
  1. Shackling Short Sellers: The 2008 Shorting Ban (2013) — link
  2. Short-Selling Bans Around the World: Evidence from the 2007-09 Crisis (2013) — link
  3. Verification Theorems for Models of Optimal Consumption and Investment with Retirement and Constrained Borrowing (2011) — link
  4. The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions (2010) — link
  5. Portfolio delegation under short-selling constraints (2006) — link
  6. Optimal Consumption-Investment Problems in Incomplete Markets with Stochastic Coefficients (2005) — link
  7. Optimal portfolios and Heston’s stochastic volatility model: an explicit solution for power utility (2005) — link
  8. Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets (2005) — link
  9. Why constrain your mutual fund manager (2004) — link
  10. A large deviations approach to optimal long term investment (2003) — link
  11. An optimal consumption model with stochastic volatility (2003) — link
  12. Differences of Opinion, Short-Sales Constraints, and Market Crashes (2003) — link
  13. Breadth of Ownership and Stock Returns (2002) — link
  14. Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints (2002) — link
  15. Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets (2002) — link
  16. Dynamic Mean-Variance Portfolio Selection with No-Shorting Constraints (2001) — link
  17. A solution approach to valuation with unhedgeable risks (2001) — link
  18. Optimal long term growth rate of expected utility of wealth (1999) — link
  19. Risk-Sensitive Dynamic Asset Management (1999) — link
  20. Consumption and Portfolio Decisions When Expected Returns are Time Varying (1999) — link
  21. Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach (1999) — link
  22. Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two‐Factor Approach (1998) — link
  23. Dynamic Nonmyopic Portfolio Behavior (1994) — link
  24. Finite Bubbles with Short Sale Constraints and Asymmetric Information (1993) — link
  25. The Risk and Predictability of International Equity Returns (1993) — link
  26. Convex Duality in Constrained Portfolio Optimization (1992) — link
  27. Optimal Dynamic Trading with Leverage Constraints (1992) — link
  28. A Duality Method for Optimal Consumption and Investment Under Short- Selling Prohibition. I. General Market Coefficients (1992) — link
  29. An Optimal Investment/Consumption Model with Borrowing (1991) — link
  30. Martingale and duality methods for utility maximization in a incomplete market (1991) — link
  31. Expected stock returns and volatility (1987) — link
  32. Debiased expert forecasts in continuous-time asset allocation (2020)
  33. Optimal portfolio policies with borrowing and shortsale constraints (2015)
  34. A note on the existence of the power investor’s optimizer (2011) — link
  35. Methods of Mathematical Finance (2010) — link
  36. Derivatives in Financial Markets with Stochastic Volatility (2000)
  37. Portfolio Selection in Stochastic Environments (1999)
  38. The Role of Learning in Dynamic Portfolio Decisions ? (1998)
  39. OPTIMAL CONSUMPTION AND PORTFOLIO SELECTION WITH INCOMPLETE MARKETS AND UPPER AND LOWER BOUND CONSTRAINTS (1994) — link
  40. Asset returns and inflation (1981)
  41. Convex Analysis (1970)

1 of 49 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.