釋迦收入保險費率釐訂之研究：應用Copula聯合機率密度函數

A Study on the Determination of the Revenue Insurance Premium Rate of Sugar Apple: Application of Copula's Joint Probability Density Function

10.3966/054696002021060109003

楊明憲(Min-Hsien Yang)；晁娜娜(Nana Chao)；楊汭華(Ruihua Yang)

農業保險 ； 收入保險 ； Copula機率分配 ； 保險費率 ； Agricultural Insurance ； Revenue Insurance ； Copula Probability Distribution ； Premium Rate

應用經濟論叢

109期（2021 / 06 / 01）

83 - 114

繁體中文

作物收入保險是農業保險發展的新趨勢，但傳統上只針對產量減損理賠的農業保險，因無法掌握產量與價格之量價關係而影響保費釐訂，且在有限資料量下依歷史模擬法估算保費，恐不能反映真實發生損失機率與幅度，從而影響保單設計與賠付率管控。釋迦收入保險為臺灣第一個作物收入保險，由於copula主要以機率的角度探討量價變數間相關與依賴關係，有助於收入保險保費之釐訂，而在臺灣農業保險文獻上卻尚未有應用此法研究，故本文即運用copula聯合機率密度函數釐訂不同保障收入和保障程度的保險費率，並與歷史模擬法進行比較分析，以期改善臺灣釋迦收入保險之設計，並提供費率釐訂之精算涵義。估計結果顯示保障程度愈高，保險費率也愈高。以100%保障而言，各地純費率均介於2.22%～8.12%之間，依基準收入換算，則每公頃保費為25,303元～95,463元。建議歷史模擬法之保費釐訂可參酌copula法在保費安全係數上予以彈性調整，即高風險地區的安全係數宜調高，而低風險地區的安全係數宜調降，以避免逆選擇並有利於作物收入保險之長期推動。

Crop revenue insurance is a new trend in the development of agricultural insurance. Since crop revenue insurance can avoid natural risks and price risks to ensure the stability of farmers' income, it has become increasingly popular abroad recently. Due to the negative correlation between output and price, this article based on the yield and price changes of Taiwanese sugar apple revenue insurance, uses the copula joint probability density function to determine the insurance premium rates at different revenue-base and degree of protection, and compares with the empirical results of historical simulation method. It is expected that findings of this article would improve the design of Taiwanese sugar apple revenue insurance, and provide the actuarial meaning of rate determination. The estimated result shows that the higher the degree of protection, the higher the insurance rate. In terms of 100% protection, the pure premium rate of each region is between 2.22% and 8.12%. Based on different revenue-base, the premium per hectare is 25,303 NT dollar to 95,463 NT dollar. The result of the copula method insurance premium rate determination is further compared with the current actual premium estimated by the historical simulation method. Because the limited yield and price data of the historical simulation method may not reflect the true probability and magnitude of loss, the premiums in high-risk areas are underestimated and low-risk areas have the problem of overestimating premiums, which may not necessarily ensure financial balance.

1. 周國端, D. G. D.(2005)。臺灣社會保險制度之實證研究–財富重分配效果分析。臺大管理論叢，15，43-70。
   連結：
2. Ahdika, A.,Rosadi, D.,Effendie, A. R.,Gunardi(2019).Modeling Indemnity of Revenue-Based Crop Insurance in Indonesia using Time-Varying Copula Models.Proceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications,Yogyakarta, Indonesia:
3. Ahmed, O.,Serra, T.(2015).Economic Analysis of the Introduction of Agricultural Revenue Insurance Contracts in Spain Using Statistical Copulas.Agricultural Economics,46,69-79.
4. Bielza, M.,Garrido, A.,Sumpsi, J. M.(2004).Revenue Insurance as an Income Stabilization Policy: An Application to the Spanish Olive Oil Sector.Cahiers d’Economie et de Sociologie Rurales,70,5-27.
5. Botts, R. R.,Boles, J. N.(1958).Use of Normal-Curve Theory in Crop Insurance Ratemaking.Journal of Farm Economics,40,733-740.
6. Coble, K. H.,Knight, T. O.,Goodwin, B. K.,Miller, M. F.,Rejesus, R. M.(2010).,United States Department of Agriculture, Risk Management Agency.
7. Cole, J. B.,Gibson, R.(2010).Analysis and Feasibility of Crop Revenue Insurance in China.Agriculture and Agricultural Science Procedia,1,136-145.
8. Dismukes, R.,Coble, K. H.(2006).Managing Risk with Revenue Insurance.Amber Waves: The Economics of Food, Farming, Natural Resources, and Rural America,4,22-27.
9. Duarte, G. V.,Braga, A.,Miquelluti, D. L.,Ozaki, V. A.(2018).Modeling of Soybean Yield Using Symmetric, Asymmetric and Bimodal Distributions: Implications for Crop Insurance.Journal of Applied Statistics,45,1920-1937.
10. Duarte, G. V.,Ozaki, V. A.(2019).Pricing Crop Revenue Insurance Using Parametric Copulas.Revista Brasileira de Economia,73,325-343.
11. Embrechts, P.,Lindskog, F.,McNeil, A.(2003).Modelling Dependence with Copulas and Applications to Risk Management.Handbook of Heavy Tailed Distributions in Finance,Amsterdan:
12. Ghosh, S.,Woodard, J. D.,Vedenov, D. V.(2011).Efficient Estimation of Copula Mixture Models: An Application to the Rating of Crop Revenue Insurance.Proceeding of Agricultural & Applied Economics Association’s 2011 AAEA & NAREA Joint Annual Meeting,Pittsburgh, Pennsylvania:
13. Glauber, J. W.(2013).The Growth of the Federal Crop Insurance Program, 1990-2011.American Journal of Agricultural Economics,95,482-488.
14. Goodwin, B. K.,Hungerford, A.(2015).Copula-Based Models of Systemic Risk in US Agriculture: Implications for Crop Insurance and Reinsurance Contracts.American Journal of Agricultural Economics,97,879-896.
15. Goodwin, B. K.,Ker, A. P.(2002).Modeling Price and Yield Risk.A Comprehensive Assessment of the Role of Risk in U.S. Agriculture,23,289-323.
16. Goodwin, B. K.,Mahul, O.(2004).Risk Modeling Concepts Relating to Design and Rating of Agricultural Insurance Contracts.Washington, DC:Work Bank Publications.
17. Goodwin, B. K.,Roberts, M. C.,Coble, K. H.(2000).Measurement of Price Risk in Revenue Insurance: Implications of Distributional Assumptions.Journal of Agricultural and Resource Economics,25,195-214.
18. Johnson, M,Tenenbein, A.(1981).A Bivariate Distribution Family with Specified Marginal.Journal of the American Statistical Association,76,198-201.
19. Just, R. E.,Weninger, Q.(1999).Are Crop Yields Normally Distributed?.American Journal of Agricultural Economics,81,287-304.
20. Miqueleto, G. J.(2011).Luiz de Queiroz College of Agriculture, University of São Paulo.
21. Nelsen, R. B.(1998).An Introductions to Copulas.New York:Springer.
22. Nonghyup Property & Casualty Insurance(2018).,Seoul:Nonghyup Property & Casualty Insurance.
23. Ramirez, O. A.,Misra, S.,Field, J.(2003).Crop-Yield Distributions Revisited.American Journal of Agricultural Economics,85,108-120.
24. Ramsey, A. F.,Ghosh, S. K.,Goodwin, B. K.(2020).Rating Exotic Price Coverage in Crop Revenue Insurance.Agricultural Finance Review,80,609-631.
25. Ramsey, A. F.,Goodwin, B. K.,Ghosh, S. K.(2019).How High the Hedge: Relationships between Prices and Yields in the Federal Crop Insurance Program.Journal of Agricultural and Resource Economics,44,227-245.
26. Sklar, A.(1959).Fonctions de Répartition à n Dimensions et Leurs Marges.Publications de l’Institut Statistique de l Université de Paris,8,229-231.
27. Tolhurst, T. N.,Ker, A. P.(2015).On Technological Change in Crop Yields.American Journal of Agricultural Economics,97,137-158.
28. United States General Accounting Office(1998).Crop Revenue Insurance: Problems With New Plan Need to Be Addressed.Washington DC:United States General Accounting Office.
29. 朱俊生, J. S,庹國柱, G. Z.(2016)。農業保險與農產品價格改革。中國金融，20，73-75。
30. 晁娜娜, N. N.,楊汭華, R. H.,羅少凡, S. F.(2017)。基於 Copula 模型的棉花收入保險費率測算研究。統計研究，34，92-99。
31. 張君, J.(2018)。吉林財經大學金融學院=School of Finance, Jilin University of Finance and Economics。
32. 庹國柱, G. Z,朱俊生, J. S.(2016)。論收入保險對完善農產品價格形成機制改革的重要性。保險研究，6，3-11。
33. 楊明憲, M. H(2017)。行政院農業委員會研究計畫行政院農業委員會研究計畫,臺北=Taipei:行政院農業委員會=Council of Agriculture, Executive Yuan。
34. 楊明憲, M. H.(2018)。韓國農業收入保險之探討與分析。農政與農情，315，78-86。
35. 楊明憲, M. H,周孟嫻, M. X.(2017)。日本農業收入保險規劃之探討與分析。農政與農情，300，72-78。
36. 農林水產省，2016，收入保險制度和農業災害賠償制度的問題和應對措施，東京：農林水產省，取自：https://www.maff.go.jp/j/study/syunyu_kento/03_shiryo/attach/pdf/kento_ 03-3.pdf，檢索日期：2016 年 11 月 30 日。(Ministry of Agriculture, Forestry and Fisheries, 2016, Issues and Directions of the Revenue Protection System and the Compensation System for Agricultural Disasters, Tokyo: Ministry of Agriculture, Forestry and Fisheries, Retrieved November 30, 2016, from https://www.maff.go.jp/j/study/syunyu_kento/03_shiryo/attach/pdf/kento_03-3.pdf.)
37. 謝鳳傑, F. J.,王爾大, E. D.,朱陽, Y.(2011)。基於 Copula 方法的作物收入保險訂價研究—以安徽省阜陽市為例。農業技術經濟，4，41-49。
38. 謝鳳傑, F. J.,吳東立, D. L.,趙思喆, S. Z.(2017)。基於 Copula 方法的大豆收入保險費率測定：理論與實證。農業技術經濟，2，111-121。