In 2000, Areshchenko won the Under 14 division of the World Youth Chess Championships, held in Oropesa del Mar, Spain, ahead of future super-grandmaster Wang Yue.

[3] In 2009 he tied for 1st–4th with Koneru Humpy, Evgenij Miroshnichenko and Magesh Panchanathan in the Mumbai Mayor Cup, which he won on a tiebreak.

[4] In the same year, he tied for first with Boris Avrukh in the Zurich Jubilee Open tournament and again won the event on a tiebreak.

[5] In 2011, Areshchenko tied for 1st–5th with Yuriy Kuzubov, Parimarjan Negi, Markus Ragger and Ni Hua in the 9th Parsvnath Open tournament.

In 2015, he tied for 1st-5th places with Nils Grandelius, Martyn Kravtsiv, Baadur Jobava and Richárd Rapport in the Masters tournament of the 22nd Abu Dhabi International Chess Festival.