Non-addictive habits: optimal consumption-portfolio policies

We formulate a model of preferences with non-addictive habits, where consumption is required to be non-negative at all times, but can fall below a “standard of living” index that aggregates past consumption. We study the consumption-portfolio problem taking account of the non-negativity constraint on consumption, and provide a constructive proof for the existence of an optimal policy on a finite time-horizon [0,T]. We show that the consumption constraint binds up to an endogenous stopping time τ∗∈[0,T], after which it remains slack until T. A decomposition of constrained consumption involving an Asian average-strike capped call-option is demonstrated.