Portfolio optimization in incomplete markets and price constraints determined by maximum entropy in the mean

TL;DR

This paper introduces a maximum entropy in the mean approach to determine asset prices in incomplete markets, ensuring they meet portfolio constraints and bid-ask ranges, with numerical analysis of portfolio returns.

Contribution

It presents a novel method using maximum entropy in the mean to set asset prices in incomplete markets consistent with market data and portfolio constraints.

Findings

Effective asset pricing method for incomplete markets

Prices conform to bid-ask ranges and portfolio constraints

Numerical results show impact on portfolio returns

Abstract

A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure is known, then the price of each asset is the discounted expected value of the asset's price under this measure. But if the market is incomplete, the risk neutral measure is not unique, and there is a range of possible prices for each asset, which can be identified with bid-ask ranges. We present in this paper an effective method to determine the current prices of a collection of assets in incomplete markets, and such that these prices comply with the cost constraints for a portfolio optimization problem. Our workhorse is the method of maximum entropy in the mean to adjust a distortion function from bid-ask market data. This distortion function plays the role of a risk neutral measure, which is used to price the assets, and the distorted probability that it determines reproduces bid-ask market values. We carry out numerical examples to study the effect on portfolio returns of the computation of prices of the assets conforming the portfolio with the proposed methodology.