Optimal Investment in an Illiquid Market with Search Frictions and Transaction Costs

Abstract

We consider an optimal investment problem to maximize expected utility of the terminal wealth, in an illiquid market with search frictions and transaction costs. In the market model, an investor's attempt of transaction is successful only at arrival times of a Poisson process, and the investor pays proportional transaction costs when the transaction is successful. We characterize the no-trade region describing the optimal trading strategy. Our asymptotic analysis implies that the effects of the transaction costs are more pronounced (more widening effect of the no-trade region and more diminishing effect of the value function) in the market with less search frictions.