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

Tae Ung Gang and Jin Hyuk Choi

Mathematical Finance, 2026, vol. 36, issue 1, 67-98

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.

Date: 2026
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