Multiplicative approximation of wealth processes involving no-short-sale strategies via simple trading

TL;DR

This paper demonstrates that in a general semimartingale market with no-short-sale constraints, wealth processes from continuous trading can be closely approximated by simple buy-and-hold strategies, facilitating practical utility maximization.

Contribution

It introduces a method to approximate continuous trading wealth processes with simple buy-and-hold strategies under no-short-sale constraints, extending practical applicability.

Findings

Wealth processes with continuous trading can be approximated by simple buy-and-hold strategies.

Optimal expected utilities from continuous trading can be approximated arbitrarily well.

The approximation relies on controlling the proportions of wealth invested in assets.

Abstract

A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy-and-hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy-and-hold strategies.