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

2024-07-18

AI Summary

This paper studies the optimal dynamic investment problem for investors in markets characterized by *both* transaction costs and search frictions—two distinct sources of illiquidity. We formulate a stochastic control model where trading is triggered by a Poisson process and agents maximize power utility. Methodologically, we develop a novel unified asymptotic framework capable of simultaneously handling arbitrarily small transaction costs and vanishing search frictions—a first in the literature. By integrating singular perturbation analysis, Poisson jump modeling, and stochastic control techniques, we derive first-order explicit asymptotic expansions for both the no-trade region boundaries and the value function along parameter curves. This result achieves the first asymptotic unification of two canonical illiquidity models—transaction-cost-based and search-friction-based—thereby enhancing analytical tractability and computational efficiency in high-dimensional illiquid settings. The framework provides new tools for empirical asset pricing and algorithmic portfolio design.

Technology Category

Search and Optimization: Mixed Discrete/Continuous SearchConstraint Satisfaction and Optimization: SearchReasoning under Uncertainty: Stochastic Optimization

Application Category

Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSocial Networks and Social Media: Social mining and social search on the Web

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.

Problem

• Optimal investment under transaction costs and search frictions
• Unified asymptotic framework for small illiquidity effects
• Deriving explicit asymptotics for no-trade region and value function

Innovation

• Novel asymptotic framework for small frictions
• Unifies transaction costs and search frictions
• Explicit asymptotics for no-trade region