This paper investigates optimal consumption and portfolio policies in continuous time under uncertainty, where asset prices follow a diffusion process. The authors propose a new approach using martingale techniques to show the existence of optimal policies without requiring compactness of admissible controls, which is a common assumption in stochastic control theory. They derive two characterization theorems and a verification theorem for optimal policies, which are counterparts of those in dynamic programming. The key advantage of their approach is that it only requires solving a linear partial differential equation, unlike the nonlinear equations typically used in dynamic programming. The paper also discusses the relationship between constrained and unconstrained solutions, showing that optimal constrained policies can be derived from unconstrained ones by incorporating insurance-like adjustments. The authors apply their framework to a special case where risky asset prices follow geometric Brownian motion, and they derive explicit formulas for optimal consumption and portfolio policies for a family of HARA utility functions. The results demonstrate that the optimal policies are linear in wealth in the unconstrained case but may differ when nonnegativity constraints are included. The paper concludes that their approach provides a more efficient and flexible method for solving optimal consumption and portfolio problems in continuous time.This paper investigates optimal consumption and portfolio policies in continuous time under uncertainty, where asset prices follow a diffusion process. The authors propose a new approach using martingale techniques to show the existence of optimal policies without requiring compactness of admissible controls, which is a common assumption in stochastic control theory. They derive two characterization theorems and a verification theorem for optimal policies, which are counterparts of those in dynamic programming. The key advantage of their approach is that it only requires solving a linear partial differential equation, unlike the nonlinear equations typically used in dynamic programming. The paper also discusses the relationship between constrained and unconstrained solutions, showing that optimal constrained policies can be derived from unconstrained ones by incorporating insurance-like adjustments. The authors apply their framework to a special case where risky asset prices follow geometric Brownian motion, and they derive explicit formulas for optimal consumption and portfolio policies for a family of HARA utility functions. The results demonstrate that the optimal policies are linear in wealth in the unconstrained case but may differ when nonnegativity constraints are included. The paper concludes that their approach provides a more efficient and flexible method for solving optimal consumption and portfolio problems in continuous time.