Convergence Rates of Turnpike Theorems for Portfolio Choice in Stochastic Factor Models

ArXiv ID: 2512.00346 “View on arXiv”

Authors: Hiroki Yamamichi

Abstract

Turnpike theorems state that if an investor’s utility is asymptotically equivalent to a power utility, then the optimal investment strategy converges to the CRRA strategy as the investment horizon tends to infinity. This paper aims to derive the convergence rates of the turnpike theorem for optimal feedback functions in stochastic factor models. In these models, optimal feedback functions can be decomposed into two terms: myopic portfolios and excess hedging demands. We obtain convergence rates for myopic portfolios in nonlinear stochastic factor models and for excess hedging demands in quadratic term structure models, where the interest rate is a quadratic function of a multivariate Ornstein-Uhlenbeck process. We show that the convergence rates are determined by (i) the decay speed of the price of a zero-coupon bond and (ii) how quickly the investor’s utility becomes power-like at high levels of wealth. As an application, we consider optimal collective investment problems and show that sharing rules for terminal wealth affect convergence rates.

Keywords: turnpike theorem, stochastic factor models, convergence rates, CRRA strategy, feedback functions

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats
• Why: The paper is heavily theoretical, involving advanced stochastic calculus, HJB equations, Malliavin calculus, and matrix Riccati equations to derive convergence rates, with no empirical data, backtests, or implementation details provided.

  flowchart TD
    A["Research Goal:<br/>Derive convergence rates<br/>of Turnpike Theorems"] --> B["Model Setup:<br/>Stochastic Factor Models<br/>with Power Utility Asymptotics"]
    B --> C{"Decomposition"}
    C --> D["Myopic Portfolios"]
    C --> E["Excess Hedging Demands"]
    D --> F["Convergence Rate Analysis"]
    E --> F
    F --> G["Rate Determinants:<br/>1. Bond Price Decay Speed<br/>2. Utility Convergence to CRRA"]
    G --> H["Application:<br/>Collective Investment<br/>Sharing Rules"]
    H --> I["Key Outcome:<br/>Quantified Convergence Speeds<br/>for Feedback Functions"]