We show an isomorphism between optimal portfolio selection or competitive equilibrium models with utilities incorporating linear habit formation, and corresponding models without habit formation. The isomorphism can be used to mechanically transform known solutions not involving habit formation...

We analyze the lifetime consumption-portfolio problem in a competitive securities market with continuous price dynamics, possibly nontradeable income, and convex trading constraints. We define a class of "translation-invariant" recursive preferences, which includes additive exponential utility,...

We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, and convex trading constraints (e.g., incomplete markets and short-sale constraints). Abstract first-order conditions of optimality are derived, based...