Prawdopodobieństwo przeżycia w modelu ryzyka z dwiema klasami ubezpieczeń

Abstract

In this paper we consider a risk model with two dependent classes of insurance business. In this model the two claim number processes are correlated. This correlation comes from the incorporation of the common process into the two claim number processes. This common process is generalized Erlang process. The claim occurrences from this common process are due to an outside factor independent of the two underlying risks, which relate to Poisson processes. The risk process with two correlated classes of business can be converted to a risk process with two new independent classes of business. The transformed process is identically distributed as the original process. Hence, the original process can be examined via this transformed process. Explicit results of non-ruin probabilities are obtained when the initial reserve is zero or when the claims sizes in the original process are exponentially distributed.