  This paper investigates the optimal investment problem in a market with two
types of illiquidity: transaction costs and search frictions. Extending the
framework established by arXiv:2101.09936, 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.
