#
Systemic Risk and Insurance Regulation ^{†}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. A Model without Systemic Risk

#### 2.1. Set Up

**Assumption**

**1:**

**Assumption**

**2:**

#### 2.2. Optimal Regulation

**Proposition**

**1.**

## 3. Regulation with Systemic Risk

#### 3.1. Extended Set Up

**Assumption**

**3:**

#### 3.2. Optimal Regulation

**Proposition**

**2.**

- Insurance companies with low exposure to systemic risk, $\rho \le {\rho}^{*}=\frac{1}{1-q}$, will be bailed out if the systemic shock occurs (i.e., $x\left(\rho \right)=1$), and are subject to a capital requirement that increases in the level of the risky exposure:$${k}_{1}^{low}\left(\rho \right)=\frac{E}{A\left(\rho \right)}=1-p\left(\theta -\frac{B}{\Delta}\right)+q\rho .$$
- Insurance companies with high exposure to systemic risk, $\rho >{\rho}^{*}$, will not be bailed out if the systemic shock occurs, and they are subject to a flat capital requirement:$${k}_{1}^{high}\left(\rho \right)=1-p(1-q)\left(\theta -\frac{B}{\Delta}\right).$$

#### 3.3. Room for Further Public Intervention

#### 3.4. Implementation of Optimal Prudential Policy

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1 | Although the systemic risk in the insurance sector clearly remains below that in the banking sector, a number of insurance firms were subsequently among the financial institutions designated as globally and systemically important (International Association of Insurance Supervisors, IAIS 2013). |

2 | The FSB is an international organization that was created by the G-20 in April 2009. Its purpose is to monitor the finance industry and to make recommendations for addressing systemic risk (see FSB 2013). |

3 | An example of this kind of intervention is the Troubled Asset Relief Program (TARP) implemented by the US in 2008. |

Regulation | $\mathit{\rho}\le {\mathit{\rho}}^{*}$ | $\mathit{\rho}>{\mathit{\rho}}^{*}$ |
---|---|---|

Technical reserves: | Actuarially fair | Actuarially fair |

Capital req.: | ${k}_{1}^{low}\left(\rho \right)=1-{\rho}_{0}+q\rho $ | ${k}_{1}^{high}\left(\rho \right)=1-(1-q){\rho}_{0}$ |

Guarantee fund: | Industry-managed | Industry-managed |

Premium $=(1-p)R\left(\rho \right)$ | Premium $=(1-p+pq)R\left(\rho \right)$ | |

Bailout mech.: | Access bailout support | No access |

Premium $=qp\frac{\rho}{{\rho}_{0}}R\left(\rho \right)$ | None |

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**MDPI and ACS Style**

Gómez, F.; Ponce, J. Systemic Risk and Insurance Regulation ^{†}. *Risks* **2018**, *6*, 74.
https://doi.org/10.3390/risks6030074

**AMA Style**

Gómez F, Ponce J. Systemic Risk and Insurance Regulation ^{†}. *Risks*. 2018; 6(3):74.
https://doi.org/10.3390/risks6030074

**Chicago/Turabian Style**

Gómez, Fabiana, and Jorge Ponce. 2018. "Systemic Risk and Insurance Regulation ^{†}" *Risks* 6, no. 3: 74.
https://doi.org/10.3390/risks6030074