Existence of a Radner equilibrium in a model with transaction costs. (arXiv:1702.01706v1 [q-fin.MF])

We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity. After establishing the existence of a discrete-time equilibrium, we show that the discrete-time equilibrium converges to a continuous-time equilibrium model. The continuous-time equilibrium provides an explicit formula for the equilibrium interest rate in terms of the transaction cost parameter. We show analytically that the interest rate can be either increasing or decreasing in the transaction costs depending on the agents' risk parameters.