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The Collaborative International Dictionary
On one's own account

Account \Ac*count"\, n. [OE. acount, account, accompt, OF. acont, fr. aconter. See Account, v. t., Count, n.,

  1. ] 1. A reckoning; computation; calculation; enumeration; a record of some reckoning; as, the Julian account of time.

    A beggarly account of empty boxes.
    --Shak.

  2. A registry of pecuniary transactions; a written or printed statement of business dealings or debts and credits, and also of other things subjected to a reckoning or review; as, to keep one's account at the bank.

  3. A statement in general of reasons, causes, grounds, etc., explanatory of some event; as, no satisfactory account has been given of these phenomena. Hence, the word is often used simply for reason, ground, consideration, motive, etc.; as, on no account, on every account, on all accounts.

  4. A statement of facts or occurrences; recital of transactions; a relation or narrative; a report; a description; as, an account of a battle. ``A laudable account of the city of London.''
    --Howell.

  5. A statement and explanation or vindication of one's conduct with reference to judgment thereon.

    Give an account of thy stewardship.
    --Luke xvi. 2.

  6. An estimate or estimation; valuation; judgment. ``To stand high in your account.''
    --Shak.

  7. Importance; worth; value; advantage; profit. ``Men of account.''
    --Pope. ``To turn to account.''
    --Shak.

    Account current, a running or continued account between two or more parties, or a statement of the particulars of such an account.

    In account with, in a relation requiring an account to be kept.

    On account of, for the sake of; by reason of; because of.

    On one's own account, for one's own interest or behalf.

    To make account, to have an opinion or expectation; to reckon. [Obs.]

    This other part . . . makes account to find no slender arguments for this assertion out of those very scriptures which are commonly urged against it.
    --Milton.

    To make account of, to hold in estimation; to esteem; as, he makes small account of beauty.

    To take account of, or to take into account, to take into consideration; to notice. ``Of their doings, God takes no account.''
    --Milton .

    A writ of account (Law), a writ which the plaintiff brings demanding that the defendant shall render his just account, or show good cause to the contrary; -- called also an action of account.
    --Cowell.

    Syn: Narrative; narration; relation; recital; description; explanation; rehearsal.

    Usage: Account, Narrative, Narration, Recital. These words are applied to different modes of rehearsing a series of events. Account turns attention not so much to the speaker as to the fact related, and more properly applies to the report of some single event, or a group of incidents taken as whole; as, an account of a battle, of a shipwreck, etc. A narrative is a continuous story of connected incidents, such as one friend might tell to another; as, a narrative of the events of a siege, a narrative of one's life, etc. Narration is usually the same as narrative, but is sometimes used to describe the mode of relating events; as, his powers of narration are uncommonly great. Recital denotes a series of events drawn out into minute particulars, usually expressing something which peculiarly interests the feelings of the speaker; as, the recital of one's wrongs, disappointments, sufferings, etc.

Wiktionary
on one's own account

adv. 1 (context idiomatic English) On one's own behalf. 2 (context idiomatic English) By oneself. 3 (context idiomatic English) At one's own risk.