Utility maximisation and time-change
Abstract
We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem, we consider an initial enlargement of filtration and we derive change of variable formulas for stochastic integrals w.r.t. a time-changed Brownian motion. The change of variable formulas allow us to shift the problem to a maximisation problem under the enlarged filtration for models driven by a Brownian motion and a finite variation process. The latter could be solved by using martingale methods. Then applying again the change of variable formula, we derive the optimal strategy for the original problem for a power utility under certain assumptions on the finite variation process of the semimartingale.
Keywords
Cite
@article{arxiv.1912.03202,
title = {Utility maximisation and time-change},
author = {Giulia Di Nunno and Hannes Haferkorn and Asma Khedher and Michèle Vanmaele},
journal= {arXiv preprint arXiv:1912.03202},
year = {2024}
}
Comments
The results presented in Section 4.3 are wrong. In particular $G_t$ introduced in Theorem 4.6 is not a filtration and hence the optimisation problem cannot be solved using the results in this theorem