Optimal investment in illiquid market with search frictions and transaction costs

TL;DR

This paper analyzes an optimal investment strategy in an illiquid market with search frictions and transaction costs, deriving the no-trade region and asymptotic effects of small transaction costs on the investor's utility.

Contribution

It introduces a model combining search frictions and transaction costs, characterizes the no-trade region, and provides asymptotic expansions for small transaction costs.

Findings

No-trade region characterized for the model.

Asymptotic expansions show increased impact of transaction costs.

Effects of transaction costs are more pronounced with market frictions.

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. We provide asymptotic expansions of the boundaries of the no-trade region and the value function, for small transaction costs. The asymptotic analysis implies that the effects of the transaction costs are more pronounced.