1. **State the problem:** Calculate the impact of inflation on the reserves for contents-only insurance using cumulative paid amounts, closed claim counts, and projected future claims inflation. 2. **Given data:** - Cumulative paid amounts (€) by underwriting year and development year: - 2020: 347 (year 2), 1024 (year 3), 1134 (year 4) - 2021: 563 (year 2), 1653 (year 3) - 2022: 806 (year 2) - Cumulative closed claim counts: - 2020: 56 (year 2), 163 (year 3), 180 (year 4) - 2021: 89 (year 2), 258 (year 3) - 2022: 125 (year 2) - Projected future claims inflation: 15% for 2023 and 2024 3. **Formula and approach:** - Reserves are the difference between ultimate claims and paid claims. - Ultimate claims = (Cumulative paid amount) / (Proportion of claims closed) - Proportion of claims closed = (Cumulative closed claim counts) / (Ultimate claim counts) - Adjust reserves for inflation by applying projected inflation rates to future payments. 4. **Calculate ultimate claims for each underwriting year:** - For 2020, latest development year 4: Ultimate claims = Cumulative paid amount at year 4 = 1134 - For 2021, latest development year 3: Ultimate claims = Cumulative paid amount at year 3 = 1653 - For 2022, latest development year 2: Ultimate claims = Cumulative paid amount at year 2 = 806 5. **Calculate proportion of claims closed for each underwriting year at latest development year:** - 2020: Closed claims = 180 - 2021: Closed claims = 258 - 2022: Closed claims = 125 6. **Calculate average claim size for each underwriting year:** - 2020: Average claim size = $\frac{1134}{180} = 6.3$ - 2021: Average claim size = $\frac{1653}{258} \approx 6.41$ - 2022: Average claim size = $\frac{806}{125} = 6.448$ 7. **Calculate reserves (ultimate claims - paid claims) at latest development year:** - 2020: Reserve = $1134 - 1134 = 0$ - 2021: Reserve = $1653 - 1653 = 0$ - 2022: Reserve = $806 - 806 = 0$ Since reserves at latest development year are zero, we consider reserves at earlier development years to estimate future payments. 8. **Calculate reserves at development year 2 for each underwriting year:** - 2020: Reserve = $1134 - 347 = 787$ - 2021: Reserve = $1653 - 563 = 1090$ - 2022: Reserve = $806 - 0 = 806$ (assuming no payments before year 2) 9. **Adjust reserves for inflation:** - Inflation applies to future payments from 2023 and 2024, i.e., development years beyond 2022. - For 2020 and 2021, future payments occur in 2023 and 2024. - For 2022, future payments occur in 2024. 10. **Calculate inflation factors:** - For payments in 2023: $1 + 0.15 = 1.15$ - For payments in 2024: $1 + 0.15 + 0.15 = 1.3225$ (compound inflation) 11. **Apply inflation to reserves:** - 2020 reserve (payments in 2023 and 2024): split equally for simplicity - Inflation adjusted reserve = $\frac{787}{2} \times 1.15 + \frac{787}{2} \times 1.3225 = 393.5 \times 1.15 + 393.5 \times 1.3225 = 452.525 + 520.038 = 972.563$ - 2021 reserve (payments in 2023 and 2024): similarly - Inflation adjusted reserve = $\frac{1090}{2} \times 1.15 + \frac{1090}{2} \times 1.3225 = 545 \times 1.15 + 545 \times 1.3225 = 626.75 + 720.0125 = 1346.7625$ - 2022 reserve (payments in 2024 only): - Inflation adjusted reserve = $806 \times 1.3225 = 1065.985$ 12. **Calculate impact of inflation on reserves:** - 2020: $972.563 - 787 = 185.563$ - 2021: $1346.7625 - 1090 = 256.7625$ - 2022: $1065.985 - 806 = 259.985$ 13. **Total impact of inflation on reserves:** $$185.563 + 256.7625 + 259.985 = 702.31$$ **Final answer:** The impact of inflation on the reserves is approximately 702.31 euros.