 It is arguable whether the function should have been called Powers-Gerber-Shiu function due to the contribution of Powers.In Powers’ notation, this is defined as

where formula_19 is the discounting force of interest, formula_20 is a general penalty function reflecting the economic costs to the insurer at the time of ruin, and the expectation formula_21 corresponds to the probability measure formula_22.The function is called expected discounted cost of insolvency in Powers.