On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance
Joint Authors
Kuznetsov, Dmitry
Kasumo, Christian
Kasozi, Juma
Source
Journal of Applied Mathematics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-02-22
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We consider an insurance company whose reserves dynamics follow a diffusion-perturbed risk model.
To reduce its risk, the company chooses to reinsure using proportional or excess-of-loss reinsurance.
Using the Hamilton-Jacobi-Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation (VIDE) which we transform into a linear Volterra integral equation (VIE) of the second kind.
We then proceed to solve this linear VIE numerically using the block-by-block method for the optimal reinsurance policy that minimizes the ultimate ruin probability for the chosen parameters.
Numerical examples with both light- and heavy-tailed distributions are given.
The results show that proportional reinsurance increases the survival of the company in both light- and heavy-tailed distributions for the Cramér-Lundberg and diffusion-perturbed models.
American Psychological Association (APA)
Kasumo, Christian& Kasozi, Juma& Kuznetsov, Dmitry. 2018. On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance. Journal of Applied Mathematics،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1176090
Modern Language Association (MLA)
Kasumo, Christian…[et al.]. On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance. Journal of Applied Mathematics No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1176090
American Medical Association (AMA)
Kasumo, Christian& Kasozi, Juma& Kuznetsov, Dmitry. On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance. Journal of Applied Mathematics. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1176090
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176090