An elementary approach to the Merton problem

In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black–Scholes–Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write down candidate value function and use verification argument prove that solution problem. However, features of take it outside standard settings stochastic control, existing proofs rely on parameter restrictions (especially, but not only, ), space admissible strategies, or intricate approximation arguments. purpose paper show these complications can be overcome using simple elegant involving perturbation utility function.