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3298. Ruin probability of the insurer-reinsurer quota-share model with phase-type distributed claims
Invited abstract in session TD-2: New Tools in Insurance Risk Management , stream OR in Banking, Finance and Insurance: New Tools for Risk Management.
Tuesday, 14:30-16:00Room: Glassalen (building: 101)
Authors (first author is the speaker)
| 1. | Marek Teuerle
|
| Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology |
Abstract
In this work, we consider a bivariate risk process describing the capitals over time of two insurance companies that share premiums and claims with fixed proportion. Such a model can be used in modeling of the capital for the insurer-reinsurer system with proportional reinsurance [1-5]. Our main results include a formula for the ruin probability of insurer or reinsurer in the infinite time for phase-type distributed claims [5]. Additionally, we will introduce two alternative methods for approximating the aforementioned ruin probability: De Vylder-type and diffusion approximations [2,4]. The accuracy of our results is validated using both synthetic and empirical data [2-5].
[1] F. Avram, Z. Palmowski, M. Pistorius (2008). A two-dimensional ruin problem on the positive quadrant. Insurance: Mathematics and Economics 42(1), 227-234
[2] K.Burnecki, M.Teuerle, A.Wilkowska (2019). De Vylder type approximation of the ruin probability for the insurer-reinsurer model, Mathematica Applicanda 47(1), 5-24
[3] K.Burnecki, M.Teuerle, A.Wilkowska (2021) Ruin probability for the insurer-reinsurer model for exponential claims, Risks 9(5), 86
[4] K.Burnecki, M.Teuerle, A.Wilkowska (2022). Diffusion approximations of the ruin probability for the insurer–reinsurer model driven by a renewal process. Risks 10(6), 129
[5] K.Burnecki, Z. Palmowski, M.Teuerle, A.Wilkowska (2023). Ruin probability for the quota share model with phase-type distributed claims.https://arxiv.org/abs/2303.07705
Keywords
- Risk Analysis and Management
- Financial Modelling
- Stochastic Models
Status: accepted
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