Stochastic differential games with inside information

TL;DR

This paper analyzes stochastic differential games involving jump diffusions with inside information, providing a characterization of Nash equilibria using advanced anticipative calculus techniques, with applications in insider finance strategies.

Contribution

It introduces a novel approach using anticipative stochastic calculus to characterize Nash equilibria in insider stochastic differential games with jump diffusions.

Findings

Characterization of Nash equilibria via Hamiltonians.

Application to insider finance problems like consumption and portfolio optimization.

Framework accommodating model uncertainty in insider trading scenarios.

Abstract

We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida-Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.