Probabilistic approach to risk processes with level-dependent premium rate

Denisov, D. E. and Gotthard, N and Korshunov, Dmitry and Wachtel, Vitali (2024) Probabilistic approach to risk processes with level-dependent premium rate. Insurance: Mathematics and Economics, 118. pp. 143-156. ISSN 0167-6687

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Abstract

We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift. We show that such risk processes give rise to heavy-tailed ruin probabilities whatever the distribution of the claim size, even if it is a bounded random variable. So, the risk processes with near critical premium rate provide an important example of a stochastic model where light-tailed input produces heavy-tailed output.