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研究生:黃義郡
研究生(外文):HUANG, YI-CHUN
論文名稱:Panel Regression Model應用於職業災害保險精算
論文名稱(外文):The Panel Regression Model Applied to Occupational Accident of Labor Insurance
指導教授:張智凱張智凱引用關係
指導教授(外文):CHANG,CHIH-KAI
口試委員:余清祥英家慶
口試委員(外文):YING, JIA-CHING
口試日期:2017-06-25
學位類別:碩士
校院名稱:逢甲大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:59
中文關鍵詞:職業災害保險可信度理論Bühlmann-Straub Credibility TheoryPanel Regression Model
外文關鍵詞:Panel Regression ModelBühlmann-Straub Credibility TheoryOccupational Accident of Labor InsuranceCredibility Theory
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現今台灣勞工保險職業災害保險費率的計算方法是依各行業經驗費率和前次釐訂的費率(現行費率)加權平均,其加權係數是以各行業別人數與全體投保人數之比例計算,且各行業別費率與現行費率差異不得超過20%,此計算方法與古典可信度理論(Classical Credibility)有所差異。古典可信度理論則以各行業別人數與過去理賠經驗變動程度計算人數之比例作為加權係數,若該行業別過去理賠變動較為平穩則加權係數較高。相較之下,台灣計算各行業別的加權係數皆低於古典可信度理論,故反應過去理賠經驗的比重較低,費率不易調整,在實際理賠資料有時間趨勢的情況下,費率將會產生顯著的誤差。除了上述兩個方法之外,Bühlmann-Straub可信度模型被廣泛應用於費率的釐訂,Bühlmann-Straub的模型是簡化貝氏理論的線性模型,相較於古典可信度理論,可以分析行業別之間風險的差異性。
本文以上述三種精算模型分別估計平均理賠,實證結果顯示,Bühlmann-Straub模型估計的平均理賠與實際值誤差最小。此外觀察職業災害保險實際的理賠資料,發現各行業別的理賠具有不同的時間趨勢,本文進一步針對Bühlmann-Straub模型加入時間因子估計費率,並藉由Panel Regression Model計算其可信度係數,不僅可考量過去的平均理賠經驗,也可以加入其他影響費率估計因子。本研究除了以Panel Regression Model估計保費之外,將逐步說明模型配適的過程,探討資料異質性處理、變數的固定與隨機效果、篩選屬於離群值的行業別。本文所提出的Panel Regression Model加入時間因子後預測之平均理賠更為精準。

Currently, the Occupational Accident of Labor Insurance premium rate is divided into the business category to pricing in Taiwan. The premium rate combined experience rate with the manual rate for each business category. There are differences between calculation method of premium rate in Taiwan and the classical credibility theory is the calculation method of the weighting factor. In Taiwan, the weighting factor is defined as the number of insured in the business category divided by the number of insured in all business categories. However, the weighting factor of the classical credibility theory is defined as the number of insured in the business category divided by standards for full credibility which are calculated in terms of the expected number of insured. If fluctuation of the claims in the past is relatively stable, the weighting factor is higher. In contrast, Taiwan's weighting factor is lower than the weighting factor of classical credibility theory. Therefore, the premium rate will have lower experience claims weight to cause the premium rate will be adjusted hard. When the claim has time trend, the estimated claims will have significant errors. In addition to the two methods above, the Bühlmann-Straub credibility model which considers an unobserved risk type of insureds is widely used in the determination of the premium rate. Compared to the classical credibility theory, the Bühlmann-Straub model could handle heteroscedastic claims distributions, trend effects, and nested classification.
This paper applies three credibility models to estimate claims, then we find the Bühlmann-Straub model estimate claims error is minimized. Moreover, the actual data show that the claims of each business categories have different time trends. Therefore, we incorporate the time trends into the Bühlmann-Straub model and use the panel regression model to estimate the credibility factor. The panel regression model can not only consider the average claims in the past, but also add other factors. In conclusion, the results show that the panel regression model incorporates the time factor to accurately estimate claims.

目錄
第一章 研究動機與方法
第二章 精算模型
第三章 資料描述與費率分析
第一節、 資料描述
第二節、 費率分析
第四章 Panel Regression Model Analysis
第一節、 變數分析
第二節、 模型選擇
第三節、 可信度與預測模型
第四節、 行業別合併議題
第五章 結論與建議
參考文獻
附錄一 行業別分類說明
附錄二 可信度係數
附錄三 各行業別最適可信度方法比較表
附錄四 隨機效果參數估計值
附錄五 R程式碼


(1)Badi H. Baltagi and James M. Griffin, 1997, “Pooled estimators vs. their heterogeneous counterparts in the context of dynamic demand for gasoline,” Journal of Econometrics, Volume 77, Issue 2, April 1997, Pages 303-327
(2)Bühlmann, H. 1967. “Experience Rating and Credibility,” Astin Bulletin 4: 199 –207
(3)Clifford F. Thies and Thomas Sturrock, 1988, “The Pension-Augmented Balance Sheet,” The Journal of Risk and Insurance, Vol. 55, No. 3 (Sep., 1988), pp. 467-480
(4)Edward W. Frees, Virginia R. Young and Yu Luo (2001), “Case Studies Using Panel Data Models,” North American Actuarial Journal, Volume 5, Number 4
(5)Gilbert W. Fellingham PhD , H. Dennis Tolley ASA, PhD and Thomas N. Herzog ASA, PhD (2013), “Comparing Credibility Estimates of Health Insurance Claims Costs,” North American Actuarial Journal, 9:1, 1-12
(6)Ilsoon Shin , Jun-Byoung Oh and Kwan Hyung Yi, 2010, “Workers' Compensation Insurance and Occupational Injuries,” Safety and Health at Work, Volume 2, Issue 2, June 2011, Pages 148–157
(7)João Victor Issler, Luiz Renato Lima, 2009, “A panel data approach to economic forecasting The bias-corrected average forecast,” Journal of Econometrics, Volume 152, Issue 2, October 2009, Pages 153–164
(8)Johannes Ledolter, Stuart Klugman, and Chang-Soo Lee (2001), “Credibility Models with Time-Varying Trend Components,” Astin Bulletin, Vol 21, No 1
(9)Mary Weiss, 1985, “A Multivariate Analysis of Loss Reserving Estimates in Property-Liability Insurers,” The Journal of Risk and Insurance, Vol. 52, No. 2 (Jun., 1985), pp. 199-221
(10)Michael M. Barth, Robert W. Klein and Gregory Krohm, 2008, “Workers’ Compensation Insurance Experience Rating and Subsequent Employer Claims: The Wisconsin Experience,” Journal of Insurance Issues, Vol. 31, No. 1 (SPRING 2008), pp. 16-42
(11)張智凱 (2014)。〈勞工保險職業災害保險費率精算及財務評估〉。行政院勞動部勞工保險局。
(12)蔡惠玲 (2012)。〈勞工保險職業災害保險費率精算〉,行政院勞工委員會勞工保險局。
(13)勞工保險條例

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