Asrian participated in several Chess Olympiads, taking home two team gold medals and one individual silver medal. He was a crucial member of the Armenian team that won the 2006 Chess Olympiad. Individually, he earned five prizes in the 2000 European Chess Championship, the best being the 7th place.
He also represented his country in the European Team Chess Championship and won silver in 2007. Moreover, he won the Dubai Open Chess Championship in 2001. In his country, he was awarded the title of "Honoured Master of Sport", reflecting his contribution to chess.
Asrian died suddenly on June 9, 2008 at the age of 28, from a heart attack while driving in Yerevan, Armenia. His death was a significant loss to Armenian chess, with thousands attending his funeral.