I present an explicitly solved equilibrium model for the distribution of wealth and income in an incomplete-markets economy. I flrst propose a self-insurance model with an inter-temporally dependent preference (Uzawa (1968), Lucas and Stokey (1984), and Obstfeld (1990)). I then derive an analytical consumption rule which captures stochastic precautionary saving motive and generates stationary wealth accumulation. Finally, I provide a complete characterization for the equilibrium cross-sectional distribution of wealth and income in closed form by developing a recursive formulation for the moments of the distribution of wealth and income. Using this recursive formulation, I show that income persistence and the degree of wealth mean reversion are the main determinants of wealth-income correlation and relative dispersions of wealth to income, such as skewness and kurtosis ratios between wealth and income.