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

[thumbnail of Ruin_critical]
Text (Ruin_critical) - Accepted Version
Download (0B)
[thumbnail of Ruin_critical]
Text (Ruin_critical) - Accepted Version
Restricted to Repository staff only until 1 January 2040.
Available under License Creative Commons Attribution.

Download (0B)
[thumbnail of Ruin_critical]
Text (Ruin_critical)
Ruin_critical.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (397kB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Insurance: Mathematics and Economics
Uncontrolled Keywords:
Research Output Funding/no_not_funded
Subjects:
?? no - not fundednoeconomics and econometricsstatistics and probabilitystatistics, probability and uncertainty ??
ID Code:
221329
Deposited By:
Deposited On:
13 Jun 2024 14:45
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 01:18