Existence and uniqueness of equilibrium in Lucas’ asset pricing model when utility is unbounded

This note presents a proof of the existence of a unique equilibrium in a Lucas (Econometrica 46(6):1429–1445, 1978) economy when the utility function displays constant relative risk aversion, and the logarithm of dividends follow a normally distributed autoregressive process of order one with positive autocorrelation. We provide restrictions on the coefficient of relative risk aversion, the discount factor and the conditional variance of the consumption process that ensure the existence of a unique equilibrium.