Topics in collective risk theory

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Collective risk theory, as a part of insurance, deals with stochastic models of an insurance business. In such a model, the occurrence of the claims is described by a point process and the amount of money that an insurer has to pay due to a claim, as a random variable. Within this stochastic rather that deterministic view of the world, risk is a key concept. The probability of ruin, the surplus prior to ruin and the deficit at the time of ruin are just some of the quantities that measure the risk of an insurance business.