Unified Asymptotics for Investment Under Illiquidity: Transaction Costs and Search Frictions

Abstract

This paper investigates the optimal investment problem in a market with two types of illiquidity: transaction costs and search frictions. We analyze a power-utility maximization problem where an investor encounters proportional transaction costs and trades only when a Poisson process triggers trading opportunities. We show that the optimal trading strategy is described by a no-trade region. We introduce a novel asymptotic framework applicable when both transaction costs and search frictions are small. Using this framework, we derive explicit asymptotics for the no-trade region and the value function along a specific parametric curve. This approach unifies existing asymptotic results for models dealing exclusively with either transaction costs or search frictions.