How do I prove the following equation:
P(X=100)≤(P(X=110)-P(X=90))/2
I am not sure how to start and whether it involves using the Black-Sholes formula or not (something like this: https://www.youtube.com/watch?v=LM6iMfHbQDs&t=939s). Also, please note that this is an option price of a put, not a probability.
Thank you!