Investment and Consumption with Regime-Switching Discount Rates

TL;DR

This paper studies how changing discount rates in a stochastic financial market affect optimal consumption and investment strategies, introducing subgame perfect strategies to handle time inconsistency caused by regime switches.

Contribution

It models regime-dependent discount rates and characterizes subgame perfect strategies in a continuous-time stochastic setting with Markov switching.

Findings

Time preference significantly influences investment strategies.

Subgame perfect strategies differ from pre-commitment strategies under regime switching.

Numerical results illustrate the impact of discount rate changes on decision-making.

Abstract

This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switch 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 a Markov chain. Following Ekeland and Pirvu we introduce and characterize the subgame perfect strategies. Numerical experiments show the effect of time preference on subgame perfect strategies and the pre-commitment strategies.