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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Probabilistic approach to risk processes with level-dependent premium rate
AU - Denisov, D. E.
AU - Gotthard, N
AU - Korshunov, Dmitry
AU - Wachtel, Vitali
PY - 2024/9/30
Y1 - 2024/9/30
N2 - 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.
AB - 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.
U2 - 10.1016/j.insmatheco.2024.06.002
DO - 10.1016/j.insmatheco.2024.06.002
M3 - Journal article
VL - 118
SP - 143
EP - 156
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
ER -