Portfolio Time Consistency and Utility Weighted 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.