 In Gerber and Shiu’s notation, it is given as

where formula_19 is the discounting force of interest and formula_25 is a penalty function capturing the economic costs to the insurer at the time of ruin (assumed to depend on the surplus prior to ruin formula_26 and the deficit at ruin formula_27), and the expectation formula_21 corresponds to the probability measure formula_22.Here the indicator function formula_30 emphasizes that the penalty is exercised only when ruin occurs.It is quite intuitive to interpret the expected discounted penalty function.