There exists one potential source which has not obtained full treatment in the recent consumption literature: a negative wealth constraint (NWC). An economic agent who faces the NWC can borrow up to a certain proportion of the present value of labor income. We present an analytically tractable...

We develop a new dynamic continuous-time model of optimal consumption and investment to include independent stochastic labor income. We reduce the problem of solving the Bellman equation to a problem of solving an integral equation. We then explicitly characterize the optimal consumption and...