Risk theory in a stochastic economic environment

We introduce a general model to describe the risk process of an insurance company. This model allows for stochastic rate of return on investments as well as stochastic level of inflation, thus in theory enabling a decision maker to choose between insurance and investment risk. In the first part of the paper we discuss the model in itself and in the second part the problem of finding the probability of eventual ruin is posed. We obtain some integro-differential equations that in some cases lead us to the exact probability of eventual ruin and in other cases to inequalities. Examples are given showing that stochastic economic factors may have a serious impact on this probability.

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