Optimal Consumption and Investment with Fixed and Proportional Transaction Costs

TL;DR

This paper investigates the optimal investment and consumption strategies over an infinite horizon considering both fixed and proportional transaction costs, providing theoretical results and numerical illustrations.

Contribution

It extends classical models by incorporating both fixed and proportional costs and proves weak dynamic programming and comparison results for viscosity solutions.

Findings

Numerical experiments reveal properties of optimal strategies.

Theoretical framework accommodates discontinuous viscosity solutions.

Analysis includes general utility functions.

Abstract

The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming is proved in the general setting and a comparison result for possibly discontinuous viscosity solutions of the dynamic programming equation is provided. Detailed numerical experiments illustrate several properties of the optimal investment strategies.