Optimal insider control and semimartingale decompositions under enlargement of filtration

TL;DR

This paper introduces new methods for representing semimartingale decompositions under enlarged filtrations using stochastic control, white noise analysis, and Hida-Malliavin calculus, with explicit examples.

Contribution

It combines advanced stochastic calculus techniques to derive novel representations of semimartingale decompositions in the context of filtration enlargement.

Findings

New representations of semimartingale decompositions

Explicit examples illustrating the methods

Integration of stochastic control and white noise analysis

Abstract

We combine stochastic control methods, white noise analysis and Hida-Malliavin calculus applied to the Donsker delta functional to obtain new representations of semimartingale decompositions under enlargement of filtrations. The results are illustrated by explicit examples.