Unified Asymptotics For Investment Under Illiquidity: Transaction Costs And Search Frictions

TL;DR

This paper develops a unified asymptotic analysis for optimal investment strategies in markets with both transaction costs and search frictions, providing explicit approximations for the no-trade region and value function.

Contribution

It introduces a novel asymptotic framework that combines transaction costs and search frictions, extending prior models to a more comprehensive setting.

Findings

Explicit asymptotics for the no-trade region

Explicit asymptotics for the value function

Unification of existing models for 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. 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.