Abstract
Delbaen and Haezendonck [Ins. Math. Econ. 6 (1987) 85] and Willmot [Scand. Actuarial J. 1 (1989) 1] give an analytical expression for the net premium density of a compound Poisson present value risk (CPPVR) process. Their calculation is based, essentially, on the independence of the increments of the CPPVR process. In this paper, under regularity conditions, we derive the first two moments of a compound renewal present value risk (CRPVR) process using renewal theory arguments. Some examples, extensions and limiting results are also given.
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