Explanation
When a derivative transaction is entered into, its value generally is close to zero. Over time, as the value of the underlying changes, the transaction acquires a positive or negative value. It is not possible to predict the future value of the transaction in advance, however distributional assumptions can be made and potential exposure can be measured in multiple ways. Of all the possible future exposures, it is generally positive exposures that are relevant to credit risk because that is the only situation where the bank may lose money from a default of the counterparty.
The maximum (generally a quantile eg, the 97.5th quantile) exposure possible over the time of the transaction is the 'Potential Future Exposure', or PFE.
The average of the distribution of positive exposures at a specified date before the longest trade in the portfolio is called 'Expected Exposure', or EE.
The expected positive exposure calculated as the weighted average of the future positive Expected Exposure across a time horize is called the EPE, or the 'Expected Positive Exposure'.
The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date - is the 'fair value', as defined under FAS 157.
Therefore the corect answer is that EPE is the weighted average of the future positive expected exposure across a time horizon.