Optimal portfolios for different anticipating integrals under insider information

TL;DR

This paper compares different anticipating stochastic integrals in a portfolio optimization problem with insider information, highlighting their suitability for deriving meaningful investment strategies.

Contribution

It analyzes and compares the Russo-Vallois, Ayed-Kuo, and Hitsuda-Skorokhod integrals in a non-adapted portfolio optimization context, revealing their practical differences.

Findings

Forward integral yields a financially meaningful portfolio

Ayed-Kuo and Hitsuda-Skorokhod integrals are less suitable for this problem

Comparison clarifies potential applications of these integrals in finance

Abstract

We consider the non-adapted version of a simple problem of portfolio optimization in a financial market that results from the presence of insider information. We analyze it via anticipating stochastic calculus and compare the results obtained by means of the Russo-Vallois forward, the Ayed-Kuo, and the Hitsuda-Skorokhod integrals. We compute the optimal portfolio for each of these cases with the aim of establishing a comparison between these integrals in order to clarify their potential use in this type of problem. Our results give a partial indication that, while the forward integral yields a portfolio that is financially meaningful, the Ayed-Kuo and the Hitsuda-Skorokhod integrals do not provide an appropriate investment strategy for this problem.