Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility

TL;DR

This paper derives explicit solutions for optimal investment and consumption strategies considering small transaction costs with general structures, using dynamic programming and singular perturbation methods, under CRRA utility.

Contribution

It introduces a novel approach to obtain closed-form solutions for portfolio optimization with complex transaction costs using advanced mathematical techniques.

Findings

Closed-form solutions for small transaction costs

Effective handling of both fixed and proportional costs

Enhanced understanding of transaction cost impacts on strategies

Abstract

Transaction costs play a critical role in asset allocation and consumption strategies in portfolio management. We apply the methods of dynamic programming and singular perturbation expansion to derive the closed-form leading solutions to this problem for small transaction costs with arbitrary transaction cost structure by maximizing the expected CRRA (constant relative risk aversion) utility function for this problem. We also discuss in detail the case which consists of both fixed and proportional transaction costs.