EXISTENCE AND UNIQUENESS OF OPTIMAL CONSUMPTION AND PORTFOLIO RULES IN A CONTINUOUS-TIME FINANCE MODEL WITH HABIT FORMATION AND WITHOUT SHORT SALES

This paper studies the solution to optimal consumption and portfolio r ules in a continuous-time finance model in which short sales are prohi bited. In this model the preference of the agent exhibits habit format ion and consumption durability which captures the effect of past consu mption choices on current utility. It is demonstrated that any continu ous, non-decreasing and concave utility function dominated by a linear function admits a solution. Furthermore, when the utility function is strictly concave, the optimal solution is unique.