Mystic Messenger was released in July/August of 2016. In April 2016, the top 5 wealthiest people in South Korea were (exchange rates calculated 7/27/17):
1) Lee Kun-Hee: ₩14.1 billion/$12.6 billion
2) Suh Kyung-Bae: ₩9.4 billion/$8.4 billion
3) Jay Y. Lee: ₩6.9 billion/$6.2 billion
4) Kwon Hyuk-Bin: ₩5.5 billion/$4.9 billion
5) Chung Mong-Koo: ₩5.3 billion/$4.8 billion
Since Jaehee says that Chairman Han is in the top 5, he’s likely not the richest person, but he’s definitely a multi-billionaire.
These numbers fluctuate quite a bit (Lee Kun-Hee is now worth ₩18.8 billion/$16.8 billion, a huge increase). If we assume the mysme universe is similar to our own in terms of wealth, around the time of release, Chairman Han himself was probably worth between ₩9.4 billion - ₩5.3 billion, or $8.4 billion - $4.8 billion.
tl;dr Jumin Han is one hell of a trust fund kid.