Investment-consumption problem
= Investment-consumption problem
{title2=$V=\sup\mathbb E\int_0^\infty e^{-\rho t}U(c_t)\,dt$}
An investment-consumption problem chooses portfolio holdings and consumption to maximize discounted <expected utility maximization> subject to a <self-financing portfolio> wealth equation and admissibility constraints. A <Hamilton-Jacobi-Bellman equation> or <utility duality with martingale deflators> characterizes the optimum when the value is finite.