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If I'm a company who pays my employees and my supply chain with my own currency created on a block chain and they can spend it wherever it is accepted, would I need a POW or POS scheme to maintain the veracity of the ledger of transactions? Or is there a way to validate the transactions and history of the ledger via centralized control? Could it work like this:

  1. Only my company could create my currency, so there's no way to counterfeit it.
  2. Everyone who accepts my currency uses software at the point of sale that verifies the transaction and the history of the ledger.
  3. Each unit of currency is embedded with personal ID that transfers to the next person with their personal ID until it eventually recycles back to me, the issuer.

Would I be able to eliminate double spending and fraud in a centralized system without the miners?

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Sure. You just use a database that keeps track of who has how much money. You can do this any way you want. You don't need anything fancy like POW, POS, or even a blockchain. The only reason you would need or want these things is to permit decentralized operation without a central authority. If you are the central authority, what you say is law just because you said it. So no need for anything fancy.

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Actually there is a centralized block-chain currency Ripple. It is made by a single centered organization which want to reduce the international money transfer charges through wire transfer. There are many big banks backing it up. It is going to change the international money transfer fees drastically. You can research more about it, just search for Ripple in Google.

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The blockchain is necessary to find consensus among an open set of participants. If you're doing a centralized blockchain, you can just do away with the blockchain. You already have a single source of truth which can operate on the basis of a regular database.

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