Turnpike Property and Convergence Rate for an Investment and Consumption Model

TL;DR

This paper investigates the turnpike property in optimal investment and consumption models, identifying key thresholds and conditions for its occurrence, and analyzing convergence rates with practical examples.

Contribution

It establishes a threshold-based criterion for the turnpike property in investment policies and explores its absence in consumption policies, with convergence rate analysis and examples.

Findings

Turnpike property depends on a threshold related to model parameters.

Turnpike property holds for investment but generally not for consumption.

Convergence rates are provided with numerical illustrations.

Abstract

We discuss the turnpike property for optimal investment and consumption problems. We find there exists a threshold value that determines the turnpike property for investment policy. The threshold value only depends on the Sharpe ratio, the riskless interest rate and the discount rate. We show that if utilities behave asymptotically like power utilities and satisfy some simple relations with the threshold value, then the turnpike property for investment holds. There is in general no turnpike property for consumption policy. We also provide the rate of convergence and illustrate the main results with examples of power and non-HARA utilities and numerical tests.