Titolo: Utility maximisation and change of variable formulas for time-changed dynamics
Abstract:
We target the problem of expected utility maximisation of the terminal wealth in a semimartingale setting, where the semimartingale is written in terms of a time-changed Brownian motion and a finite variation process. As for the time-change we consider a general increasing stochastic process with finitely many jumps.
To tackle this problem we present change of variable formulas for stochastic integrals w.r.t. the time-changed Brownian motion and we use techniques of enlargement of filtrations. The focus is on power and logarithmic utility.
The presentation is based on joint work with Hannes Haferkorn (Commerzbank), Asma Khedher (U. Amsterdam), and Michèle Vanmaele (U. Ghent).