Abstract
We show how existing results for optimal trading strategies with linear temporary price impact/exponential resilience or proportional transaction costs
can be easily adapted for the more realistic situation when the drift of the asset is unknown, so we have to project to the observable filtration generated by the asset price process, using results from non-linear filtering theory.
In particular, we observe that an arithmetic Brownian motion $P$ with unknown (constant) drift $\mu$ is the continuation of a generalized bridge process under $\mc{F}^P$ with the true drift replaced with its unbiased estimate over a fixed time window
can be easily adapted for the more realistic situation when the drift of the asset is unknown, so we have to project to the observable filtration generated by the asset price process, using results from non-linear filtering theory.
In particular, we observe that an arithmetic Brownian motion $P$ with unknown (constant) drift $\mu$ is the continuation of a generalized bridge process under $\mc{F}^P$ with the true drift replaced with its unbiased estimate over a fixed time window
| Original language | English |
|---|---|
| Journal | Risk |
| Publication status | Published - Dec 2024 |