On Investment-Consumption with Regime-Switching

TL;DR

This paper analyzes consumption and investment strategies in a stochastic economy with regime-switching discount rates, deriving equilibrium policies and examining how changes in discount rates influence investor behavior.

Contribution

It introduces and characterizes equilibrium investment and consumption policies in a regime-switching model with time-inconsistent preferences, providing closed-form solutions for logarithmic utility.

Findings

Higher discount rates increase equilibrium consumption.

Regime-switching affects investment strategies and consumption.

Numerical results illustrate the impact of time preference and risk aversion.

Abstract

In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representative investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switches according to a finite state Markov chain. The change in the discount rate leads to time inconsistencies of the investor's decisions. The randomness in our model is driven by a Brownian motion and Markov chain. Following Ekeland etc (2008) we introduce and characterize the equilibrium policies for power utility functions. Moreover, they are computed in closed form for logarithmic utility function. We show that a higher discount rate leads to a higher equilibrium consumption rate. Numerical experiments show the effect of both time preference and risk aversion on the equilibrium policies.