Portfolio Time Consistency and Utility Weighted Discount Rates

TL;DR

This paper analyzes the Merton portfolio problem with stochastic volatility and non-constant discount rates, addressing time inconsistency by characterizing subgame perfect strategies via an extended HJB equation and numerical methods.

Contribution

It introduces a novel framework incorporating utility-weighted discount rates and characterizes subgame perfect strategies through an extended HJB equation with a fixed point approach.

Findings

Time discount rate significantly influences optimal strategies.

Utility-weighted discount rate is characterized as a fixed point.

Numerical experiments illustrate strategy differences under various discount rates.

Abstract

Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider the subgame perfect strategies. The later are characterized through an extended Hamilton Jacobi Bellman (HJB) equation. A fixed point iteration is employed to solve the extended HJB equation. This is done in a two stage approach: in a first step the utility weighted discount rate is introduced and characterized as the fixed point of a certain operator; in the second step the value function is determined through a linear parabolic partial differential equation. Numerical experiments explore the effect of the time discount rate on the subgame perfect and precommitment strategies.