  This paper studies an optimal consumption-investment problem for an investor
whose instantaneous utility depends on both consumption and wealth, and the
investor faces a general borrowing constraint that the investment amount in the
risky asset does not exceed an exogenous function of the wealth. We show that
the value function is second-order smooth and present the optimal
consumption-investment policy in a feedback form. Moreover, when the risky
investment amount is bounded above by a fixed constant, we show that under
certain conditions, the constraint is binding if and only if an endogenous
threshold bounds the portfolio wealth, and we determine the endogenous wealth
threshold with the smooth fit condition. Our results encompass several
well-developed portfolio choice models and imply new applications.
