Income disaster model with optimal consumption

Abstract We propose a continuous-time income disaster model with optimal consumption. We endogenously determine the stochastic discount factor (SDF) in an incomplete market caused by income disaster. We then derive optimal consumption decisions for two types of agents, one who is exposed to income disaster and another who is not. We find a large incomplete-markets precautionary savings term between the two agents, which pushes the interest rate down and helps to resolve the risk-free rate puzzle. Interestingly, with income disaster the equilibrium interest rate is a decreasing function of risk aversion while the equity premium is an increasing function. Finally, our model can better match empirical marginal propensities to consume numbers and explain the low-consumption-high-savings puzzle.