# A Deep Learning Integrated Cairns-Blake-Dowd (CBD) Sytematic Mortality Risk Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Cairns-Blake-Dowd (CBD) Model

**Definition**

**1.**

**Lemma**

**1.**

## 3. The Neural Network Model

#### 3.1. Artificial Neural Network Definition

**Definition**

**2.**

#### 3.2. Deep Learning Modeling

**Definition**

**3.**

**Definition**

**4.**

**Lemma**

**2.**

#### 3.3. Backward Propagation of Errors

**Definition**

**5.**

**Definition**

**6.**

#### 3.4. Recurrent Neural Network Using a Long Short-Term Memory Architecture

**Proposition**

**1.**

**Proof.**

**Definition**

**7.**

**Definition**

**8.**

## 4. Mathematical Application and Results

**Proposition**

**2.**

**Proof.**

## 5. Conclusions

## 6. Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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Output | Input | |||
---|---|---|---|---|

${k}_{t}^{\left(2\right)}$ | ${k}_{t-1}^{\left(2\right)}$ | ${k}_{t-2}^{\left(2\right)}$ | .... | ${k}_{t-j}^{\left(2\right)}$ |

${k}_{t+1}^{\left(2\right)}$ | ${k}_{t}^{\left(2\right)}$ | ${k}_{t-1}^{\left(2\right)}$ | .... | ${k}_{t-j+1}^{\left(2\right)}$ |

${k}_{t+2}^{\left(2\right)}$ | ${k}_{t+1}^{\left(2\right)}$ | ${k}_{t}^{\left(2\right)}$ | .... | ${k}_{t+j-2}^{\left(2\right)}$ |

${k}_{t+3}^{\left(2\right)}$ | ${k}_{t+2}^{\left(2\right)}$ | ${k}_{t+1}^{\left(2\right)}$ | .... | ${k}_{t+j-3}^{\left(2\right)}$ |

.... | .... | .... | .... | .... |

${k}_{t+m}^{\left(2\right)}$ | ${k}_{t+m-1}^{\left(2\right)}$ | ${k}_{t+m-2}^{\left(2\right)}$ | .... | ${k}_{t+m-j}^{\left(2\right)}$ |

Nations | Number of Years | Years of Testing Set |
---|---|---|

U.K. | 1930–2018 | 1998–2018 |

Kenya | 2010–2020 | 2010–2020 |

Nation | ARIMA Model $(\mathit{p},\mathit{d},\mathit{q})$ |
---|---|

U.K. | |

Males | $ARIMA$ (1,1,0) |

Females | $ARIMA$ (1,1,0) |

Kenya | |

Males | $ARIMA$ (0,1,3) |

Females | $ARIMA$ (0,1,3) |

Nation | Males | Females | ||
---|---|---|---|---|

U.K. | MAE | RMSE | MAE | RMSE |

${k}_{t}^{\left(2\right)}$ LSTM | 2.45 | 3.54 | 2.34 | 3.65 |

${k}_{t}^{\left(2\right)}$ ARIMA | 16.56 | 22.45 | 18.45 | 24.45 |

Kenya | MAE | RMSE | MAE | RMSE |

${k}_{t}^{\left(2\right)}$ LSTM | 2.56 | 3.85 | 2.85 | 3.96 |

${k}_{t}^{\left(2\right)}$ ARIMA | 20.85 | 24.05 | 21.56 | 26.86 |

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**MDPI and ACS Style**

Odhiambo, J.; Weke, P.; Ngare, P.
A Deep Learning Integrated Cairns-Blake-Dowd (CBD) Sytematic Mortality Risk Model. *J. Risk Financial Manag.* **2021**, *14*, 259.
https://doi.org/10.3390/jrfm14060259

**AMA Style**

Odhiambo J, Weke P, Ngare P.
A Deep Learning Integrated Cairns-Blake-Dowd (CBD) Sytematic Mortality Risk Model. *Journal of Risk and Financial Management*. 2021; 14(6):259.
https://doi.org/10.3390/jrfm14060259

**Chicago/Turabian Style**

Odhiambo, Joab, Patrick Weke, and Philip Ngare.
2021. "A Deep Learning Integrated Cairns-Blake-Dowd (CBD) Sytematic Mortality Risk Model" *Journal of Risk and Financial Management* 14, no. 6: 259.
https://doi.org/10.3390/jrfm14060259