We study the risk-taking behavior of entrepreneurs in an environment with two main ingredients: finite lives and uninsurable idiosyncratic risk on the business. We show that the fraction of wealth invested in the business depends on the idiosyncratic risk premium and that it declines substantially over the life cycle. The consumption-wealth ratio is U-shaped over the life cycle. We solve for the wealth distribution both across and within age groups. We show that the variance of wealth conditional on age has an inverted-U shape, initially increasing with age and eventually declining. We find support for these predictions in the data using a survey of entrepreneurial activity in Thailand. We also consider the impact of financial development and demographic transitions on asset prices, economic activity, and inequality. We show that an increase in the fraction of idiosyncratic risk entrepreneurs can insure or a decline in population growth will lead to a reduction in the idiosyncratic risk premium, an increase in the capital stock of the economy, and a decline in inequality.