Time Consistent Portfolio Management

The Merton portfolio management problem is studied within a framework that incorporates stochastic volatility, a non-constant time discount rate, and power utility. This setting gives rise to time inconsistency, which is addressed by adopting subgame-perfect strategies. These strategies are characterized through an extended Hamilton–Jacobi–Bellman (HJB) equation, which is solved using a fixed-point iteration scheme. The solution proceeds in two stages: first, the utility-weighted discount rate is introduced and identified as the fixed point of a suitable operator; second, the value function is obtained by solving a linear parabolic partial differential equation. Numerical experiments illustrate the influence of the time-varying discount rate on subgame-perfect strategies and their outcomes.

Bio
https://ms.mcmaster.ca/~tpirvu/