Abstract, Classic, and Explicit Turnpikes

TL;DR

This paper proves three types of turnpike theorems in portfolio optimization, showing convergence of optimal portfolios and payoffs over long horizons in various stochastic models, including general semimartingales and diffusions.

Contribution

It establishes new turnpike results in a broad stochastic setting, connecting long-term optimal portfolios to myopic and ergodic solutions.

Findings

Optimal payoffs and portfolios converge under myopic probabilities.

In diffusion models, portfolios converge under the physical probability.

Finite-horizon portfolios approach a long-run myopic portfolio from ergodic HJB solutions.

Abstract

Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike states that optimal final payoffs and portfolios converge under their myopic probabilities. In diffusion models with several assets and a single state variable, the classic turnpike demonstrates that optimal portfolios converge under the physical probability; meanwhile the explicit turnpike identifies the limit of finite-horizon optimal portfolios as a long-run myopic portfolio defined in terms of the solution of an ergodic HJB equation.