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This paper considers a variant of the classical Cram\'er-Lundberg model thatis particularly appropriate in the credit context, with the distinguishingfeature that it corresponds to a finite number of obligors. The focus is oncomputing the ruin probability, i.e., the probability that the initial reserve,increased by the interest received from the obligors and decreased by thelosses due to defaults, drops below zero. Besides an exact analysis (in termsof transforms) of this ruin probability, also an asymptotic analysis isperformed, including an efficient importance-sampling based simulationapproach. The base model is extended in multiple dimensions: (i) we consider amodel in which there may, in addition, be losses that do not correspond todefaults, (ii) then we analyze a model in which the individual obligors arecoupled through a regime-switching mechanism, (iii) then we extend the modelsuch that between the losses the reserve process behaves as a Brownian motionrather than a deterministic drift, and (iv) we finally consider a set-up withmultiple groups of statistically identical obligors.

A transient Cram\'er-Lundberg model with applications to credit risk