# Measuring Systemic Governmental Reinsurance Risks of Extreme Risk Events

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Systemic Excess Loss Reinsurance Model

**Z**), which gives the expected value of reinsurance-dependent claims ${Z}_{1},{Z}_{2},\dots ,{Z}_{n}$. Because $E\left(Z\right)=E\left(X\right)-E\left(Y\right)$, we can consider the expectation of $Y$, which is given by:

#### 3.2. Systemic Proportional Reinsurance

#### 3.3. Monte Carlo Simulation

## 4. Results

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Tail conditional expectation of the reinsurer’s aggregate risks, for different quantile levels. Panel (

**a**) shows the conditional tail expectation of the aggregate loss, assuming positive-dependent and independent risks. Panel (

**b**) shows the difference in the tail conditional expectation between positive-dependent and independent risks, for various quantile levels.

Risk 1 | Risk 2 | Risk 3 | Risk 4 | Risk 5 | Risk 6 | Risk 7 | Risk 8 | Risk 9 | Risk 10 |
---|---|---|---|---|---|---|---|---|---|

1.000 | 0.904 | 0.890 | 0.920 | 0.885 | 0.924 | 0.932 | 0.929 | 0.901 | 0.903 |

0.904 | 1.000 | 0.895 | 0.859 | 0.865 | 0.889 | 0.893 | 0.945 | 0.938 | 0.859 |

0.890 | 0.895 | 1.000 | 0.903 | 0.909 | 0.918 | 0.939 | 0.883 | 0.909 | 0.861 |

0.920 | 0.859 | 0.903 | 1.000 | 0.876 | 0.920 | 0.889 | 0.917 | 0.865 | 0.864 |

0.885 | 0.865 | 0.909 | 0.876 | 1.000 | 0.894 | 0.927 | 0.894 | 0.870 | 0.918 |

0.924 | 0.889 | 0.918 | 0.920 | 0.894 | 1.000 | 0.890 | 0.933 | 0.891 | 0.900 |

0.932 | 0.893 | 0.939 | 0.889 | 0.927 | 0.890 | 1.000 | 0.927 | 0.925 | 0.869 |

0.929 | 0.945 | 0.883 | 0.917 | 0.894 | 0.933 | 0.927 | 1.000 | 0.933 | 0.900 |

0.901 | 0.938 | 0.909 | 0.865 | 0.870 | 0.891 | 0.925 | 0.933 | 1.000 | 0.865 |

0.903 | 0.859 | 0.861 | 0.864 | 0.918 | 0.900 | 0.869 | 0.900 | 0.865 | 1.000 |

Percentile | Risk 1 | Risk 2 | Risk 3 | Risk 4 | Risk 5 | Risk 6 | Risk 7 | Risk 8 | Risk 9 | Risk 10 |
---|---|---|---|---|---|---|---|---|---|---|

Independent insurance claims | ||||||||||

10% | 0.005 | 0.008 | 0.010 | 0.005 | 0.005 | 0.005 | 0.007 | 0.006 | 0.003 | 0.006 |

25% | 0.006 | 0.010 | 0.011 | 0.006 | 0.006 | 0.006 | 0.008 | 0.007 | 0.003 | 0.007 |

50% | 0.008 | 0.012 | 0.014 | 0.008 | 0.008 | 0.007 | 0.010 | 0.009 | 0.004 | 0.009 |

75% | 0.010 | 0.016 | 0.019 | 0.011 | 0.010 | 0.010 | 0.014 | 0.012 | 0.005 | 0.012 |

90% | 0.013 | 0.021 | 0.024 | 0.014 | 0.013 | 0.013 | 0.018 | 0.016 | 0.007 | 0.015 |

Positive-Dependent insurance claims | ||||||||||

10% | 0.019 | 0.030 | 0.034 | 0.019 | 0.019 | 0.018 | 0.025 | 0.022 | 0.010 | 0.022 |

25% | 0.022 | 0.035 | 0.039 | 0.022 | 0.022 | 0.021 | 0.029 | 0.026 | 0.012 | 0.025 |

50% | 0.030 | 0.047 | 0.053 | 0.030 | 0.029 | 0.029 | 0.040 | 0.035 | 0.016 | 0.034 |

75% | 0.047 | 0.072 | 0.082 | 0.046 | 0.045 | 0.045 | 0.062 | 0.055 | 0.024 | 0.051 |

90% | 0.072 | 0.109 | 0.126 | 0.070 | 0.069 | 0.069 | 0.096 | 0.086 | 0.036 | 0.078 |

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**MDPI and ACS Style**

Hadad, E.; Shushi, T.; Yosef, R.
Measuring Systemic Governmental Reinsurance Risks of Extreme Risk Events. *Risks* **2023**, *11*, 50.
https://doi.org/10.3390/risks11030050

**AMA Style**

Hadad E, Shushi T, Yosef R.
Measuring Systemic Governmental Reinsurance Risks of Extreme Risk Events. *Risks*. 2023; 11(3):50.
https://doi.org/10.3390/risks11030050

**Chicago/Turabian Style**

Hadad, Elroi, Tomer Shushi, and Rami Yosef.
2023. "Measuring Systemic Governmental Reinsurance Risks of Extreme Risk Events" *Risks* 11, no. 3: 50.
https://doi.org/10.3390/risks11030050