Compared to the distributions of earnings, the distributions of wealth in the US and many other countries are strikingly concentrated on the top and skewed to the right. To explain the income and wealth inequality, we provide a tractable heterogeneous‐agent model with incomplete markets in continuous time. We separate illiquid capital assets from liquid bond assets and introduce jump risks to capital income, which are crucial for generating a thicker tail of the wealth distribution than that of the labor income distribution. Under recursive utility, we derive optimal consumption and wealth in closed form and show that the stationary wealth distribution has an exponential right tail that closely approximates a power‐law distribution. Our calibrated model can match the income and wealth distributions in the US data including the extreme right tail of the wealth distribution.