# Disruption of Life Insurance Profitability in the Aftermath of the COVID-19 Pandemic

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## Abstract

**:**

## 1. Introduction

## 2. Profit Resilience in Annuity

- ${P}_{x}$ is the pure premium based on the first-order mortality basis table;
- R is the constant instalment paid by the insurance company during the policyholder’s life with a value agreed at contract time;
- ${l}_{x}$ is the number of policyholders at age x deduced by the first-order mortality basis table used to compute the pure premium;
- i is the technical rate;
- $\omega $ is the extreme age, thus $\omega -1$ is the last age for a policyholder and ${l}_{\omega}=0$.

- ${R}_{0}$ is the first instalment defined at contract time.

- ${R}_{t}$ is the instalment at time t if the policyholder is alive;
- ${R}_{t-1}$ is the instalment at time $t-$1 if the policyholder is alive;
- ${r}_{t}$ is the downgraded rate of return used to vary the rate based on the segregated fund return rate using the following formula:

- ${g}_{t}$ is the segregated fund return rate for the period ($t-1,t$) recognised at time t;
- $mt$ is the rate retained by the insurance company on the segregated fund return;
- $mg$ is the minimum guaranteed rate of the segregated fund.

- $\alpha $ is the loading rate of the annuity payment;
- $\beta $ is the loading rate of the administrative costs.

- ${E\left(U\right)}_{x,k}$ is the present expected profit at time k when the contract is purchased by an individual at age x;
- ${PT}_{x,k}$ is the expenses loaded premium at time k for a policyholder at age x; ${BE}_{x,k}$ is the best estimate of the contract liability a time k for a policyholder at age x according to Solvency II principles, by considering the financial options and guarantees to include in the insurance contract;
- ${CoC}_{x,k}$ is the cost of capital due to the allocation of the capital requirement under Solvency II for a contract sold a time k for a policyholder at age x.
- Cost of capital, ${CoC}_{x,k}$, is determined according to Solvency II requirements:

- ∂ is the cost of capital rate increase;
- ${i}_{rf}\left(k,k+l\right)$ is the risk-free rate for the time horizon $\left(k,k+l\right)$;
- C is the cost of capital rate, that is, the unrealised extra-return compared to the risk-free rate;
- ${SCR}_{x,k+l-1}$ is the solvency capital requirement for the time horizon $k+l-1$ and a policyholder of age x;
- m is the number of years when the risk expires in terms of capital requirements.

- ${r}_{t}$ is the short-term interest rate at time t;
- $\alpha $ is the mean-reverting force of the shocks;
- $\beta $ is the long-term interest rate mean;
- $\sigma $ is the market volatility;
- ${Z}_{t}$ is a Wiener process.

## 3. Numerical Application

#### 3.1. Demographic Scenario

- $\alpha \left(x\right)$ is the expected proportion of deaths by COVID-19 at age x;
- $\rho (x,t)$ is the expected loss of years of life expectancy at age x and time t.

#### 3.2. Financial Scenario

#### 3.3. Cash Flow Analysis

#### 3.4. Focus on Profitability

#### 3.5. Discussion

## 4. Concluding Remarks

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | https://www.mortality.org/, accessed on 28 September 2021. |

2 | https://www.epicentro.iss.it/coronavirus/sars-cov-2-decessi-italia, accessed on 5 October 2021. |

3 | https://www.istat.it/it/archivio/240401, accessed on 5 October 2021. |

4 | https://www.eurex.com/ex-en/, accessed on 25 September 2021. |

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**Figure 3.**$BE$ distribution for the baseline and accelerated mortality tables for age 20 (EUR/thousands).

**Figure 4.**$BE$ distribution for baseline and accelerated mortality tables for age 40 (EUR/thousands).

**Figure 5.**$BE$ distribution for baseline and accelerated mortality tables for age 60 (EUR/thousands).

Parameter | Estimation |
---|---|

$\alpha $ | 0.00069 |

$\beta $ | 1.20514 |

$\sigma $ | 0.48054 |

Variable | Notation | Values |
---|---|---|

Contract years | k | 2022, 2024, 2026, 2032 |

Policyholder ages | x | 20, 40, 60 |

Mortality table | ${l}_{x}$ | A62I unisex with 50% male and 50% female |

Initial annual instalment | ${R}_{0}$ | EUR 1000 |

Technical rate | i | 0% |

Guaranteed minimum rate | ${m}_{g}$ | 0% |

Retained rate | ${m}_{t}$ | 1% |

Loading rate for instalment payment | $\alpha $ | 1.50% |

Loading rate for administrative costs | $\beta $ | 5% |

Annual management costs at time t | EUR 0.50 | |

Annual inflation of management costs | 2% | |

Cost of capital increasing rate | ∂ | 1.00 |

Cost of capital rate | C | 6% |

Year | 2022 | 2022 | 2022 | 2022 | 2022 | 2022 | 2022 | 2022 | 2022 |
---|---|---|---|---|---|---|---|---|---|

Demographic Table | Base | Base | Base | Accelerated | Accelerated | Accelerated | Difference | Difference | Difference |

Individual Age | 20 | 40 | 60 | 20 | 40 | 60 | 20 | 40 | 60 |

$PT$ | 73,064 | 52,302 | 31,917 | 73,064 | 52,302 | 31,971 | 0 | 0 | 0 |

$BE$ | 65,844 | 44,896 | 25,806 | 66,767 | 44,822 | 25,735 | −77 | −74 | −71 |

$SCR$ | 5867 | 3433 | 2475 | 5792 | 3416 | 2451 | −75 | −17 | −24 |

$CoC$ | 11,584 | 4886 | 2465 | 11,516 | 4852 | 2178 | −68 | −34 | −287 |

$E\left(U\right)$ | −4364 | 2521 | 3646 | −4219 | 2628 | 4004 | 145 | 107 | 358 |

$E\left(U\right)/PT$ | −6.0% | 4.8% | 11.4% | −5.8% | −5.0% | −12.5% | 0.2% | 0.2% | 1.1% |

$RORAC=E\left(U\right)/SCR$ | −74.4% | 73.4% | 147.3% | −72.8% | 76.9% | 163.4% | 1.5% | 3.5% | 16.1% |

t | Base 20 | Accelerated 20 | Base 40 | Accelerated 40 | Base 60 | Accelerated 60 |
---|---|---|---|---|---|---|

1 | 1051 | 1051 | 1050 | 1050 | 1046 | 1046 |

2 | 1051 | 1051 | 1050 | 1050 | 1041 | 1041 |

3 | 1052 | 1052 | 1051 | 1051 | 1036 | 1036 |

4 | 1053 | 1053 | 1051 | 1051 | 1030 | 1030 |

5 | 1054 | 1054 | 1051 | 1051 | 1023 | 1023 |

6 | 1054 | 1054 | 1051 | 1051 | 1016 | 1016 |

7 | 1055 | 1055 | 1051 | 1051 | 1008 | 1008 |

8 | 1056 | 1056 | 1050 | 1050 | 1000 | 1000 |

9 | 1057 | 1057 | 1050 | 1050 | 990 | 990 |

10 | 1057 | 1058 | 1049 | 1049 | 980 | 979 |

11 | 1058 | 1059 | 1049 | 1049 | 969 | 968 |

12 | 1059 | 1060 | 1048 | 1048 | 956 | 956 |

13 | 1060 | 1061 | 1047 | 1047 | 943 | 942 |

14 | 1061 | 1062 | 1046 | 1046 | 928 | 927 |

15 | 1062 | 1063 | 1045 | 1045 | 911 | 910 |

16 | 1063 | 1064 | 1043 | 1043 | 893 | 892 |

17 | 1063 | 1066 | 1041 | 1041 | 873 | 871 |

18 | 1064 | 1067 | 1039 | 1039 | 851 | 849 |

19 | 1065 | 1068 | 1036 | 1036 | 827 | 825 |

20 | 1066 | 1069 | 1033 | 1033 | 800 | 797 |

30 | 1070 | 1080 | 975 | 975 | 387 | 372 |

40 | 1056 | 1077 | 806 | 805 | 36 | 34 |

50 | 997 | 1029 | 395 | 383 | 19 | 17 |

70 | 401 | 416 | 19 | 19 | 0 | 0 |

90 | 20 | 21 | 0 | 0 | 0 | 0 |

100 | 0 | 0 | 0 | 0 | 0 | 0 |

Year | 2024 | 2024 | 2024 | 2024 | 2024 | 2024 | 2024 | 2024 | 2024 |
---|---|---|---|---|---|---|---|---|---|

Demographic Table | Base | Base | Base | Accelerated | Accelerated | Accelerated | Difference | Difference | Difference |

Individual Age | 20 | 40 | 60 | 20 | 40 | 60 | 20 | 40 | 60 |

$PT$ | 73,063.66 | 52,302.43 | 31,916.68 | 73,063.66 | 52,302.43 | 31,916.68 | 0.00 | 0.00 | 0.00 |

$BE$ | 66,473.08 | 45,310.30 | 26,085.22 | 66,391.41 | 45,233.16 | 26,011.08 | −81.67 | −77.15 | −74.15 |

$SCR$ | 5967.65 | 3473.89 | 2496.08 | 5892.18 | 3456.21 | 2471.78 | −75.47 | −17.68 | −24.30 |

$CoC$ | 11,828.06 | 4971.35 | 2233.67 | 11,757.23 | 4936.24 | 2213.17 | −70.84 | −35.11 | −20.49 |

$E\left(U\right)$ | −5237.49 | 2020.77 | 3597.79 | −5084.98 | 2133.03 | 3692.43 | 152.51 | 112.26 | 94.64 |

$E\left(U\right)/PT$ | −7.2% | 3.9% | 11.3% | −7.0% | 4.1% | 11.6% | 0.2% | 0.2% | 0.3% |

RORAC = E(U)/SCR | −87.8% | 58.2% | 144.1% | −86.3% | 61.7% | −149.4% | 1.5% | 3.5% | 5.2% |

Year | 2026 | 2026 | 2026 | 2026 | 2026 | 2026 | 2026 | 2026 | 2026 |
---|---|---|---|---|---|---|---|---|---|

Demographic Table | Base | Base | Base | Accelerated | Accelerated | Accelerated | Difference | Difference | Difference |

Individual Age | 20 | 40 | 60 | 20 | 40 | 60 | 20 | 40 | 60 |

$PT$ | 73,063.66 | 52,302.43 | 31,916.68 | 73,063.66 | 52,302.43 | 31,916.68 | 0.00 | 0.00 | 0.00 |

$BE$ | 67,114.49 | 45,732.18 | 26,368.39 | 67,028.23 | 45,651.28 | 26,290.94 | −86.25 | −80.90 | −77.45 |

$SCR$ | 6070.58 | 3515.85 | 2517.68 | 5994.27 | 3497.69 | 2493.14 | −76.31 | −18.17 | −24.54 |

$CoC$ | 12077.99 | 5058.48 | 2270.46 | 12,003.72 | 5022.09 | 2249.39 | −74.27 | −36.40 | −21.07 |

$E\left(U\right)$ | −6128.82 | 1511.77 | 3277.82 | −5968.30 | 1629.07 | 3376.35 | 160.52 | 117.30 | 98.52 |

$E\left(U\right)/PT$ | −8.4% | 2.9% | 10.3% | −8.2% | 3.1% | 10.6% | 0.2% | 0.2% | 0.3% |

RORAC = E(U)/SCR | −101.0% | 43.0% | 130.2% | −99.6% | 46.6% | 135.4% | 1.4% | 3.6% | 5.2% |

Year | 2032 | 2032 | 2032 | 2032 | 2032 | 2032 | 2032 | 2032 | 2032 |
---|---|---|---|---|---|---|---|---|---|

Demographic Table | Base | Base | Base | Accelerated | Accelerated | Accelerated | Difference | Difference | Difference |

Individual Age | 20 | 40 | 60 | 20 | 40 | 60 | 20 | 40 | 60 |

$PT$ | 73,063.66 | 52,302.43 | 31,916.68 | 73,063.66 | 52,302.43 | 31,916.68 | 0.00 | 0.00 | 0.00 |

$BE$ | 69,134.24 | 47,057.37 | 27,254.28 | 69,033.10 | 46,964.43 | 27,166.33 | −101.14 | −92.94 | −87.95 |

$SCR$ | 6395.46 | 3648.20 | 2585.94 | 6316.43 | 3628.56 | 2560.78 | −79.03 | −19.64 | −25.16 |

$CoC$ | 12867.52 | 5332.32 | 2385.92 | 12782.22 | 5291.93 | 2363.12 | −85.29 | −40.39 | −22.80 |

$E\left(U\right)$ | −8938.10 | −87.26 | 2276.48 | −8751.67 | 46.07 | 2387.24 | 186.43 | 133.32 | 110.76 |

$E\left(U\right)/PT$ | −12.2% | −0.2% | 7.1% | −12.0% | 0.1% | 7.5% | 0.3% | 0.3% | 0.3% |

RORAC = E(U)/SCR | −139.8% | −2.4% | 88.0% | −138.6% | 1.3% | 93.2% | 1.2% | 3.7% | 5.2% |

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**MDPI and ACS Style**

Carannante, M.; D’Amato, V.; Fersini, P.; Forte, S.; Melisi, G.
Disruption of Life Insurance Profitability in the Aftermath of the COVID-19 Pandemic. *Risks* **2022**, *10*, 40.
https://doi.org/10.3390/risks10020040

**AMA Style**

Carannante M, D’Amato V, Fersini P, Forte S, Melisi G.
Disruption of Life Insurance Profitability in the Aftermath of the COVID-19 Pandemic. *Risks*. 2022; 10(2):40.
https://doi.org/10.3390/risks10020040

**Chicago/Turabian Style**

Carannante, Maria, Valeria D’Amato, Paola Fersini, Salvatore Forte, and Giuseppe Melisi.
2022. "Disruption of Life Insurance Profitability in the Aftermath of the COVID-19 Pandemic" *Risks* 10, no. 2: 40.
https://doi.org/10.3390/risks10020040