  This paper studies the income fluctuation problem with capital income risk
(i.e., dispersion in the rate of return to wealth). Wealth returns and labor
earnings are allowed to be serially correlated and mutually dependent. Rewards
can be bounded or unbounded. Under rather general conditions, we develop a set
of new results on the existence and uniqueness of solutions, stochastic
stability of the model economy, as well as efficient computation of the ergodic
wealth distribution. A variety of applications are discussed. Quantitative
analysis shows that both stochastic volatility and mean persistence in wealth
returns have nontrivial impact on wealth inequality.
