We shall in this paper consider approximation of a risk reserve process by a Wiener process. Our main mathematical tool is the theory of weak convergence of probability measures on metric spaces. Today Billingsley (1968) is the standard reference for that theory. We hope that this paper is readable also for those not acquainted with Billingsley's book. To our knowledge the first application of weak convergence in risk theory is due to Iglehart (1969). In chapter 5 of Beekman (1974) some further discussions are found.
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Jan Grandell (1977) studied this question.
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