We establish rigorously the existence and properties of the stationary probability distribution which characterizes the accumulation of non-contingent ﬁnancial claims by a risk averse individual who confronts random wage fluctuations and incomplete insurance markets. We show that there exists a unique, almost-everyhwere continuous stationary cumulative distribution function which characterizes the accumulation of non-contingent ﬁnancial claims in a stochastic steady-state. This distribution is shown to possess a single mass point coinciding with the non-negative, ﬁnite borrowing limit faced by the individual. We establish that the stationary distribution which characterizes the asset accumulation of low time preference individuals is at least as large, in the sense of ﬁrst-degree stochastic dominance, as that of individuals with higher rates of time preference. We prove that, so long as individuals are allowed to borrow in amounts which can be repayed with probability one, additive diﬀerences in the probability distribution governing random wage earnings imply inversely proportional additive diﬀerences in the stationary probability distributions which govern the accumulation of non-contingent ﬁnancial claims.
Clarida, Richard H., "On the Stochastic Steady-State Behavior of Optimal Asset Accumulation in the Presence of Random Wage Fluctuations and Incomplete Markets" (1984). Cowles Foundation Discussion Papers. 934.