A new proof for a known result in risk theory

摘要

In the classical risk model, an insurer pays claim costs at the instants of their occurrence and he receives premiums in a continuous linear way. If there is no initial risk reserve, it is known that, under specified assumptions, the probability of non-ruin in the finite interval (o, t) equals1tq=1ct∫OcttF(s)ds,where tF(s) is the distribution function of the totality of claim costs in the interval (o, t) and where c is the constant rate of premium income. For (1), we refer the reader to TAKACS (1967) and to the bibliography in chapter 7 of that book. Here we give a new, rather elementary demonstration of that relation. It is possible that our method of proof allows extensions to more general situations.The reader should note that by the “global” point of view adopted in this paper, the delicate problems of measurability are solved automatically.