  Value adjustment of uncollateralized trades is determined within a
risk-neutral pricing framework. When hedging such trades, investors cannot
freely trade protection on their own name, thus facing an incomplete market.
This fact is reflected in the non-uniqueness of the pricing measure, which is
only constrained by the values of the hedging instruments tradable by the
investor. Uncollateralized trades should then be considered not as derivatives
but as new primary assets in the investor's economy. Different choices of the
risk-neutral measure correspond to different completions of the market, based
on the risk appetite of the investor, leading to different levels of value
adjustments. We recover, in limiting cases, results well known in the
literature.
