A Certainty Equivalent Merton Problem

The Merton problem is the well-known stochastic control of choosing consumption over time, as well an investment mix, to maximize expected constant relative risk aversion (CRRA) utility consumption. formulated and provided analytical solution in 1970; since then a number extensions original formulation have been solved. In this note we identify certainty equivalent problem, i.e., deterministic optimal with same value function policy, for base extensions. When time discretized, becomes second-order cone program (SOCP), readily solved using domain specific languages convex optimization. This makes it good starting point model predictive control, policy that can handle are either too cumbersome or impossible exactly standard dynamic programming methods.