Optimal investment with insider information using Skorokhod & Russo-Vallois integration

TL;DR

This paper compares Russo-Vallois and Skorokhod integrals in optimal insider trading, revealing that Skorokhod integration yields better utility, with implications for understanding anticipative stochastic calculus in finance.

Contribution

It provides a theoretical and numerical comparison of two anticipating stochastic calculus techniques in insider trading, highlighting the superior performance of Skorokhod integrals.

Findings

Skorokhod insider outperforms Russo-Vallois forward insider.

Risk-neutral traders can outperform insiders under certain fluctuations.

Anticipating calculus impacts utility outcomes in insider trading.

Abstract

We study the maximization of the logarithmic utility for an insider with different anticipating techniques. Our aim is to compare the utilization of Russo-Vallois forward and Skorokhod integrals in this context. Theoretical analysis and illustrative numerical examples showcase that the Skorokhod insider outperforms the forward insider. This remarkable observation stands in contrast to the scenario involving risk-neutral traders. Furthermore, an ordinary trader could surpass both insiders if a significant negative fluctuation in the driving stochastic process leads to a sufficiently negative final value. These findings underline the intricate interplay between anticipating stochastic calculus and nonlinear utilities, which may yield non-intuitive results from the financial viewpoint.