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 is allowed to fall below a “standard of living” index that aggregates past consumption. In this context we study the consumption-portfolio choice 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 ]. In particular, we show that the consumption constraint binds up to an endogenously determined 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.