Hello,
As per PMI PMP exam guidelines and rules which re-enforced by PerasonVue, you are not allowed to use pen or paper during the at home online PMP exam. However, you will be provided with a whiteboard along with a calculator built-in to your online exam you can easily access. Since calculators aren't allowed, I will guess that a stylus pen will not be allowed either, but the best person to ask will be your protector before you start your exam. I will recommend: 1. Arrive on time and take the time to familiarize yourself on how to use the whiteboard I personally didn't feel the need to use it when I took my PMP exam, and 2. Avoid verbally asking protector questions during your PMP exam to avoid being flagged for talking. I hope this was helpful.
Best of luck!