On asymptotic optimality of Merton's myopic portfolio strategies for discrete time market

TL;DR

This paper examines whether continuous-time Merton's portfolio strategies remain effective when applied to discrete-time markets, demonstrating that they approximate optimal performance as the time steps become very small.

Contribution

It provides theoretical analysis showing the asymptotic optimality of Merton's strategies in discrete-time settings as the discretization becomes finer.

Findings

Merton's strategy approximates the optimal discrete-time strategy with small time steps.

The performance gap diminishes as the discretization interval decreases.

The results support using continuous-time strategies in discrete models for sufficiently small intervals.

Abstract

This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the performance of the optimal strategy in a discrete time model with the sufficiently small time steps