Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs

TL;DR

This paper analyzes the impact of proportional transaction costs on optimal investment strategies over finite time horizons, deriving asymptotic expansions of the value function and proposing nearly optimal strategies.

Contribution

It provides a rigorous asymptotic analysis of the value function and develops nearly optimal strategies accounting for transaction costs in finite-time investment.

Findings

Asymptotic expansion of the value function in powers of transaction cost

Derivation of nearly optimal investment strategies

Matching utility asymptotics with leading terms

Abstract

We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost. The utility function considered is power utility. We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of transaction cost parameter. We also obtain a "nearly optimal" strategy, whose utility asymptotically matches the leading terms in the value function.