The structure of optimal portfolio strategies for continuous time markets

TL;DR

This paper demonstrates that in incomplete continuous-time markets, near-optimal portfolio strategies can be constructed using a limited set of mutual funds, effectively reducing the problem's complexity.

Contribution

It introduces a relaxed version of the Mutual Fund Theorem, enabling dimension reduction in portfolio strategies for markets with many risky assets.

Findings

Near-optimal strategies use a limited number of mutual funds

Dimension reduction simplifies complex portfolio optimization

Applicable under mild market conditions

Abstract

The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a market with a larger number of available risky stocks. In other words, a dimension reduction is achieved via a relaxed version of the Mutual Fund Theorem.