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Definition of assertion : 1. Maintenance; vindication; as, the assertion of one's rights or prerogatives.
2. The act of asserting, or that which is asserted; positive declaration or averment; affirmation; statement asserted; position advanced.

Synonyms:

financial statement, self-assertion, avouchment, asseveration, averment, self-confidence, effrontery, program line, allegation, boldness, impudence, self-reliance, affirm, confidence, trust, claim, command, arrogance, instruction

confirmation, promise, testimony, sanction, verification, certification, assurance, pledge, submission, acknowledgment, validation, declaration, proclamation, corroboration, affirmation, pronouncement, attestation, statement, oath, avowal, endorsement, warranty, approval, admission, ratification

criticism, examination, interpolation, article, dissertation, thesis, position, commentary, argument, hypothesis, research, conjecture, critique, analysis, contention, postulation, opinion, premise, essay, discussion

inference, query, presumption, matter, assumption, principle, paradigm, issue, consideration, concept, theme, subject, problem, topic, basis, exposition, motif, idea, question, theorem, text, belief, axiom, point

communication, announcement, expression, disclosure, exhibition, dissemination, broadcasting, divulging, confession, advertisement, revelation

Usage examples:

• But Mary stuck to her assertion, and at last it was decided that Una was either out of her mind, or that she was no lady. - "Only One Love, or Who Was the Heir", Charles Garvice.
• I make no positive assertion that he spent any time in watching the British; Revere, knowing the route, may have signalled in order to make sure that the news crossed the river, even though he himself might fail. - "The Siege of Boston", Allen French.
• The assertion leaped involuntarily from Diana's lips. - "The Splendid Folly", Margaret Pedler.