Portfolio Optimization in Incomplete Markets and Price Constraints Determined by Maximum Entropy in the Mean

28 Pages Posted: 30 May 2018 Last revised: 20 Jul 2018

See all articles by Argimiro Arratia

Argimiro Arratia

Polytechnic University of Catalonia (UPC)

Henryk Gzyl

Instituto de Estudios Superiores de Administración (IESA)

Date Written: May 17, 2018

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 which can be identified as the bid-ask range. We present in this paper an effective method to determine the prices of a set of assets in incomplete markets, or when the class of risk neutral measures are not known, and such that these prices comply with the cost constraints of 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.

Keywords: Econophysics; distorsion function; maximum entropy in mean; portfolio optimization; risk neutral measures; asset pricing

JEL Classification: G11, G12, G13

Suggested Citation

Arratia, Argimiro and Gzyl, Henryk, Portfolio Optimization in Incomplete Markets and Price Constraints Determined by Maximum Entropy in the Mean (May 17, 2018). Available at SSRN: https://ssrn.com/abstract=3180287 or http://dx.doi.org/10.2139/ssrn.3180287

Argimiro Arratia (Contact Author)

Polytechnic University of Catalonia (UPC) ( email )

C. Jordi Girona, 31
Barcelona, 08034
Spain

Henryk Gzyl

Instituto de Estudios Superiores de Administración (IESA) ( email )

Ave, Iesa, San Bernardino
Caracas, 1010
Venezuela

HOME PAGE: http://www.iesa.edu.ve

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
65
Abstract Views
481
rank
463,972
PlumX Metrics