Optimal portfolios of a long-term investor with floor or drawdown constraints

TL;DR

This paper investigates long-term portfolio optimization for investors with floor or drawdown constraints, revealing that such constraints do not significantly impact the asymptotic growth rate of expected utility.

Contribution

It provides a theoretical analysis showing the minimal effect of floor constraints on long-term growth and characterizes long-run optimality under these constraints.

Findings

Floor constraints do not affect asymptotic growth rate significantly.

Characterization of long-run optimality under drawdown constraints.

Convergence of finite horizon value functions to asymptotic optimal value.

Abstract

We study the portfolio selection problem of a long-run investor who is maximising the asymptotic growth rate of her expected utility. We show that, somewhat surprisingly, it is essentially not affected by introduction of a floor constraint which requires the wealth process to dominate a given benchmark at all times. We further study the notion of long-run optimality of wealth processes via convergence of finite horizon value functions to the asymptotic optimal value. We characterise long-run optimality under floor and drawdown constraints.