The General Structure of Optimal Investment and Consumption with Small Transaction Costs

TL;DR

This paper derives asymptotic formulas for optimal investment and consumption strategies in markets with small proportional transaction costs, revealing how preferences and market dynamics influence trading behavior and welfare.

Contribution

It provides a general asymptotic framework for understanding optimal policies under small transaction costs in continuous-time models with dynamic assets.

Findings

Explicit leading-order corrections for optimal policies are derived.

A dynamic model for implied trading volume is developed.

Market and preference effects on welfare are characterized.

Abstract

We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small transaction costs, we derive simple formal asymptotics for the optimal policy and welfare. These reveal the roles of the investors' preferences as well as the market and cost dynamics, and also lead to a fully dynamic model for the implied trading volume. In frictionless models that can be solved in closed form, explicit formulas for the leading-order corrections due to small transaction costs are obtained.