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In this paper we propose an extended concept of the expected discounted penalty function (EDPF) that takes into account new ruin-related random variables. In the well-known EDPF introduced in seminal papers by Gerber and Shiu (Insur Math Econ 21:129–137, 1997, N Am Actuar J 2(1):48–78, 1998) and Gerber and Landry (Insur Math Econ 22:263–276, 1998), we consider the expectation of a sequence of discounted penalty functions of new record minima reached by a claim of the risk process after ruin (and before recovery). Inspired by results of Huzak et al. (Ann Appl Probab 14(3):1378–1397, 2004) and developments in fluctuation theory for spectrally negative Lévy processes, we provide a characterization for this extended EDPF in a setting involving a cumulative claims modeled by a subordinator, and Brownian perturbation. We illustrate how the extended EDPF can be used to compute the expected discounted value of capital injections for the Brownian perturbed risk model.

On a generalization of the expected discounted penalty function to include deficits at and beyond ruin