# Reinsurance Policy under Interest Force and Bankruptcy Prohibition

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## Abstract

**:**

## 1. Introduction

## 2. The Model

## 3. Changing of Variable

**Proposition**

**1.**

**Proof.**

**Remark**

**1.**

## 4. Solving the HJB Equation

**Proposition**

**3.**

**Theorem**

**1.**

**Proof.**

**Remark**

**2.**

## 5. Numerical Example

**Example**

**1.**

**Example**

**2.**

**Example**

**3.**

**Example**

**4.**

**Example**

**5.**

**Example**

**6.**

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The optimal reinsurance policy with respect to z under different interest rates $i=0.05,0.1,0.15$.

**Figure 5.**The optimal reinsurance policy with respect to z under different volatility rates $n=0.5,1,1.5$.

**Figure 6.**The optimal reinsurance policy with respect to z with different reinsurance safety loading $\varrho =0.4,0.5,0.6$.

The Influence Factor | Insurance Retention Level |
---|---|

Time $t\uparrow $ | ↑ |

Interest rate $i\uparrow $ | ↓ |

Diffusion volatility rate $n\uparrow $ | ↓ |

Reinsurance safety loading $\varrho $↑ | ↑ |

Expected loss in unit time m↑ | ↑ |

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**MDPI and ACS Style**

Zhong, Y.; Huang, H.
Reinsurance Policy under Interest Force and Bankruptcy Prohibition. *Axioms* **2023**, *12*, 378.
https://doi.org/10.3390/axioms12040378

**AMA Style**

Zhong Y, Huang H.
Reinsurance Policy under Interest Force and Bankruptcy Prohibition. *Axioms*. 2023; 12(4):378.
https://doi.org/10.3390/axioms12040378

**Chicago/Turabian Style**

Zhong, Yangmin, and Huaping Huang.
2023. "Reinsurance Policy under Interest Force and Bankruptcy Prohibition" *Axioms* 12, no. 4: 378.
https://doi.org/10.3390/axioms12040378