臺灣博碩士論文加值系統

本文藉由台灣癌症登記中心所公布之 [1979-2011] 癌症首發率資料。 探討以癌症首發率模型之
時間參數作為癌症首發率指數並連結此指數之 K-Forwards 進行癌症首發率年代避險之避險效率。首先 , 我們透過 Lee Carter Family Model 進行癌症首發率配適以及預測。 經過研究發現效果最好的模型為 APC Model( M3 ), 其配適 1984-2008 年的 mean absolute percentage error (MAPE)為 17.02 %; 預測 2009-2011 年之 MAPE 為 6.04 % 。 顯示不論在配適及預測上 , APC Model皆可以有效的描述台灣癌症首發率。 除了中低年齡層之癌症首發率估計值與真實值相當接近之外 ,癌症首發率在高齡層之變動 ( 上升速度趨緩或下降之趨勢 ), APC Model 亦可描述此現象。 而預測2009-2011 年癌症首發率中 , 只有 2011 年在高年齡層有些許高估但癌症首發率在高年齡之變動還是有預測到。 此外 , 我們建立出連結癌症首發率指數之 K-Forwards 。 透過模擬未來 20 年之癌症首發率 , 我們比較 30 歲、 40 歲以及 50 歲 20 年定期癌症保險在四種不同避險次數避險策略之避險效率以及邊際效用。 以 30 歲 20 年期之癌症保險為例 , 每 5 年避險交易一次共交易 3 次之避險效率為 92.7% , 每 1 年避險交易一次共交易 19 次之避險效率為 98.7% ; 然而交易 19 次之邊際效用只增加為 0.4% 。 隨著避險次數之上升 , 避險效率亦跟著上升 ; 然考量邊際效用後 , 每 5 年避險一次之避險策略雖然避險交易次數最少 , 但避險效率與每 1 年避險交易一次之避險效率差異並不顯著。

Using cancer incidence rate data of the Taiwan Cancer Registry from 1979 to 2010, this study analyzed the hedge period effect of cancer incidence rate using K-Forwards, where the cancer incidence index is the time-varying parameter of the cancer incidence rate model. We first employed the Lee Carter Family Models to fit and predict the cancer incidence rate. Among the collected models, we specified that the Age Period Cohort Model (APC Model)
is optimal for modeling cancer incidence rate because of its performance in terms of mean absolute percentage error (MAPE). The MAPE of fitting [1984 　 2008] is 17.02 time-varying parameters in the APC Model to formulate a standardized cancer incidence index derivative called K-Forwards. Using the cancer incidence rate forecasted for 20 years, we compared the hedge effects of four different hedge strategies by 20-term cancer insurance in which the
policyholder is aged 30, 40, or 50 years. For the 20-term cancer insurance aged 30, the hedge effect once every five years for a total of three times was 92.7 utility was 0.4 strategy for once every five years and that for every year.

Table of Contents
1. 前言 ................................................................................. 1
2. 癌症首發率資料介紹 .................................................................. 4
3. 癌症首發率符號定義及模型介紹 ........................................................5
3.1 癌症首發率模型介紹 ..............................................................6
3.2 模型參數估計 ( 以 M1 為例 ) ..................................................... 7
3.2.1 參數估計方法介紹 .........................................................8
3.2.2 模型檢測 ................................................................. 8
3.2.3 其餘候選模型參數估計及模型檢測方法 ......................................9
3.2.4 候選模型模型挑選準則 .....................................................9
4. 候選模型配適及其預測效果 ...........................................................10
4.1 最適模型 M3 介紹 ...............................................................13
4.1.1 M3 參數估計值 .......................................................... 13
4.1.2 M3 預測成果 ............................................................ 17
5. 建立癌症首發率指數 ................................................................. 18
5.1 The New-Data-Invariant Property .............................................. 18
5.2 M3 之改良模型 M3 ∗ ............................................................ 19
5.3 改良模型 M3 ∗ 之估計效果 .......................................................20
6. K-Forwards 之避險策略 ............................................................. 22
6.1 K-Forwards 介紹 ................................................................22
6.2 K-Forwards 避險策略 ........................................................... 23
7. 模擬 K-Forwards 之避險效果 ........................................................ 27
7.1 癌症保單之計算及避險策略 ...................................................... 27
7.2 模擬之避險效果 ................................................................. 28
8. 結論 ................................................................................ 31
References .............................................................................32
附錄 A 其餘候選模型參數估計及預測效果 ................................................ 33
附錄 B 係數 Y
∗ 推導
..................................................................... 38

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