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題名:應用極值理論估算稻米颱風損失之研究
作者:伍珮瑄
作者(外文):Pei-Hsuan Wu
校院名稱:國立高雄第一科技大學
系所名稱:管理研究所
指導教授:賴麗華
學位類別:博士
出版日期:2009
主題關鍵詞:可能最大損失風險值T年水準極值分配Value-at-RiskT-year LevelExtreme Value DistributionProbable Maximum Loss
原始連結:連回原系統網址new window
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台灣地處亞熱帶地區,天然災害頻繁,常造成農業重大損失,為減輕天然災害對農民的影響,政府於1991年發布實施「農業天然災害救助辦法」,並設置「農業天然災害救助基金」以辦理各項現金救助、補助或低利貸款利息補貼所需經費,每年由農委會編列近十億元預算來挹注該基金,然而此金額相較實際損失情形顯有不足。其次,許多研究陸續提出放寬救助門檻與提高救助標準之建議,因此精確估計農業天然災害損失並了解天然救助辦法執行的情形是一項重要課題。
稻米是台灣最重要的糧食作物,而稻米所面對的天然災害以颱風的威脅最為嚴重與頻繁,本文根據「台灣農業統計年報」,使用1971年到2007年稻米颱風損失資料,先檢定與配適年損失頻率與損失幅度的分配,其次應用極值理論估算稻米遭受颱風損失情形,並且估計極端損失分配的尾部風險衡量,最後估計每年稻米颱風總損失金額。實證結果發現:(1)台灣稻米颱風損失之年損失頻率與損失幅度兩者之間是相互獨立,此結果利於年總損失的估計,可提供政府編列「農業天然災害救助基金」預算之參考。(2)年損失頻率服從Poisson分配,若不考慮極端損失的影響,損失幅度服從Log-normal或Log-gamma分配,此損失分配可提供政府制定農業天然災害損失救助金分配等級之參考或未來開辦農作物保險的費率合理精算之參考。(3)極端損失服從generalized Pareto分配,此結果有助於農業巨災門檻之界定。(4)極端損失分配的尾部風險衡量估計值,如T-year Level, VaR, ES,以及PML等,可作為政府安排高風險的救助計畫或再保險方案之參考。
Of all the weather phenomena in Taiwan, typhoons are the most catastrophic, not only their fierceness but also frequency of occurrence. From 1971 to 2007, approximately two-thirds (63%) of all natural disaster damage to rice was caused by typhoons. In order to ease the impact of natural disasters on agriculture and the farmers, Taiwan’s agricultural natural disaster assistance program (TANDAP) was passed and implemented in 1991. However, the threshold of grant-in-relief is too high relatively to actual losses of farmers and the budget seems not enough for specific years which have huge agriculture losses. Consequently, an accurate estimation of annual aggregative agriculture damage is not only a critical task for TANDAP to budget compensation plans but also an issue of concern in academic and insurance area.
This dissertation aims at understanding the connection between annual disaster losses and compensation capacity of TANDAP. The study applies 123 rice losses caused from typhoon damage to look insight into the annual frequency and losses distribution. Consequently, this study reveals the existence of independence between annual frequency and losses by individual typhoon. Therefore, a collective risk model is a feasible scheme for estimating annual aggregate losses. Next, this dissertation also focuses on using extreme value theory to fit a generalized Pareto distribution to rice damage. Some typical risk measures of extreme value distribution, such as T-year level, Value-at-Risk, expected shortfall, and probable maximum loss, are also estimated.
The results are concluded as follows. First, the annual frequency of rice damage caused by typhoons is fitted well by Poisson distribution. The loss distribution is fitted by Log-normal or Log-gamma but it fits the tail of rice loss distribution badly. Therefore, generalized Pareto distribution is used alternatively to fit the extreme losses. Second, many implications can be drawn from the tail-related risk measures of extreme value distribution. These high-quantile measures could provide useful information for Council of Agriculture (COA) to check the applicable loss compensation regulations and an adjustment of relief threshold or natural disaster relief budget plan. Last, a compound Poisson distribution or a compound binomial distribution is applicable to estimate annual aggregate rice losses.
1.Aggarwal, P. K., N. Kalra, S. H. Chander, and H. Pathak, 2006, “Info Crop: A dynamic simulation model for the assessment of crop yields losses due to pests, and environmental impact of agro-ecosystems in tropical environments,” Agricultural System, 89, 1-25.new window
2.Agresti, A., Introduction to Categorical Data Analysis, John Wiley and Sons, New York, 1996.
3.Artzner, P., F. Delbaen, J. M. Eber, D. Heath, 1997, “Thinking coherently,” Risk, 10(11), 68–71.
4.Artzner, P., F. Delbaen, J. M. Eber, D. Heath, 1999, “Coherent measures of risk,” Mathematical Finance, 9(3), 203–228.
5.Atwood, J. A., S. Shaik, and M. J. Watts, 2003, “Are crop yields normally distributed? A reexamination,” American Journal of Agricultural Economics, 85(4), 888-901.
6.Atwood, J. A., S. Shaik, and M. J. Watts, 2002, “Can normality of yields be assumed for crop insurance?” Canadian Journal of Agricultural Economics, 50(2), 171-84.
7.Babcock, B. A., and D. A. Hennessy, 1996, “Input demand under yield and revenue insurance,” American Journal of Agricultural Economics, 78, 416-27.
8.Bain, L., and M. Engelhardt, Introduction to Probability and Mathematical Statistics, Duxbury Press, Boston, 1991.
9.Balkema, A. A., and L. de Haan, 1974, “Residual life time at great age,” Annual Probability, 2, 792-804.
10.Boland, P. J., Statistical and Probabilistic Methods in Actuarial Science, Chapman and Hall, New York, 2007.
11.Bowers, N., H. Gerber, J. Hickman, D. Jones, and C. Nesbitt, Actuarial Mathematics, The Society of Actuaries, 1997.
12.Brabson, B. B., and J. P. Palutikof, 2000, “Tests of the generalized Pareto distribution for predicting extreme wind speeds,” Journal of Applied Meteorology, 39(9), 1627-1640.
13.Cebrian, A. C., M. Denuit, and P. Lambert, 2003, “Generalized Pareto fit to the society of actuaries’ large claims database,” North American Actuarial Journal, 7 (3), 10-36.
14.Chang, C. C., 2002, “The potential impact of climate change on Taiwan''s agriculture,” Agricultural Economics, 27, 51-64.
15.Chang, N. H., K. B. Ling, and L. H. Lai, Planning Farmers Welfare System-An Analysis of the Disaster Salvation of Crop in Taiwan, Council of Agriculture, Executive Yuan, Taiwan, 2001. (In Chinese)
16.Chen, C. C., and C. C. Chang, 2005, “The impact of weather on crop yield distribution in Taiwan: some new evidence from panel data models and implications for crop insurance,” Agricultural Economics, 33, 503-511.
17.Chen, C. C., and C. C. Chang, 2007, “The Analysis on the Economic Impacts of Global Warming and the Possible Adaptation Strategies in the Domestic and World Rice Markets,” Proceeding of The Economic Impacts of Global Warming in Taiwan’s Rice Market, 31-62. Taichung, Taiwan. (In Chinese)
18.Chen, C. C., B. A. McCarl, C. C. Chang, 2008, “Stronger El Niño/Southern Oscillation Events and the Economics of the International Rice Market,” Climate Research, 36, 113-122.
19.Cherng, J. C., 1995, “A Study on Pure Rate of Rice Disaster Insurance in Taiwan,” Thesis of Master, Department of Applied Economics, National Chung Hsing University, Taiwan. (In Chinese)
20.Christofides, S., C. Barlow, N. Michaelides, and C. Miranthis, 1992, “Storm rating in the nineties,” General Insurance Convention, Bournemouth, UK.
21.Chu, L. F., C. C. Chen, and H. J. Chen, 2007, “An Estimation of Rice Damage Function by Typhoon and the Premium Calculation of Disaster Insurance in Taiwan,” Taiwanese Agricultural Economic Review, 13(1), 37-67. (In Chinese)new window
22.Coble, K. H., T. O. Knight, R. D. Pope, and J. R. Williams, 1996, “Modeling Farm-Level crop insurance demand with panel data,” American Journal of Agricultural Economics, 78, 439-47.
23.Coles, S., and L. Pericchi, 2003, “Anticipating catastrophes through extreme value modeling,” Applied Statistics, 52(4), 405-416.
24.Coles, S., An introduction to statistical modeling of extreme values, Springer, New York, 2001.
25.Davison, A.C., and R.L. Smith, 1990, “Models for exceedances over high thresholds (with discussion),” Journal of the Royal Statistical Society, Series B, Methodological, 52, 393-442.
26.Embrechts, P., S. I. Resnick, and G. Samorodnitsky, 1999, “Extreme value theory as a risk management tool,” North American Actuarial Journal, 3(2), 32-41.
27.Embrechts P., C. P. Kl¨uppelberg, and T. Mikosh, Modelling Extremal Events, Springer-Verlag, Berlin, 1997.
28.Engeland, K., H. Hisdal, and A. Frigessi, 2004, “Practical Extreme Value Modelling of Hydrological Floods and Droughts: A Case Study,” Extremes, 7(1), 5-30.new window
29.Fisher, R. A., and L. H. C. Tippett, 1928, “Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample,” Proceedings of the Cambridge Philosophical Society, 24, 180-190.
30.Food and Agriculture Organization of the United Nations Web: http://www.fao.org/.
31.Gertensgarbe, F. W., and P. C. Werner, 1989, “A method for the statistical definition of extreme-value regions and their application to meteorological time series,” Zeitschrift fur Meteorologie, 39, 224-226.
32.Gilli, M., and E. Kellezi, 2006, “An application of extreme value theory for measuring financial risk,” Computational Economics, 27, 207–228.
33.Hansen, L. M., 2004, “Economic damage threshold model for pollen beetles (Meligethes aeneus F.) in spring oilseed rape (Brassica napus L.) Crops,” Crop Protection, 23(1), 43-46.new window
34.Hartington, A. W., M. Falcone, W. J. K. Mulcahy, J. E. Skinner, S. Fisher, J. E. Sayers, and L. F. Waters, 1997, “Catastrophe Modeling,” General Insurance Convention 1997, Blackpool, UK.
35.Hennessy, D. A., B. A. Babcock, and D .J. Hayes, 1997, “Budgetary and producer welfare effects of revenue insurance,” American Journal of Agricultural Economics, 79, 1024-34.
36.Hogg, R., and S. Klugman, Loss Distributions, Wiley, New York, 1984.
37.Hosking, J. R. M., and J. F. Wallis, 1987, “Parameter and quantile estimation for the generalized Pareto distribution,” Technometrics, 29, 339-349.
38.Huigen, M. and I. C. Jens, 2006, “Socio-Economic Impact of Super Typhoon Harurot in San Mariano, Isabela, the Philippines,” World Development, 34(12), 2116-2136.
39.Jenkinson, A. F., 1955, “The Frequency Distribution of the Annual Maximum (or minimum) Values of Meteorological elements,” Quarterly Journal of the Royal Meteorology Society, 87, 145-158.
40.Ji, Q. Z., S. Hayakawa, H. Yamamoto, N. Okada, and H. Tatano, 2002, “Comparisons of agricultural damages by typhoon 9917, 9919 and 9918,” Japanese Journal of Crop Science, 71(2), 239-249.
41.Jorion, P., Value at Risk, McGraw-Hill, New York, 2007.
42.Just, R. E., and Q. Weninger, 1999, “Are Crop Yields Normally Distributed?” American Journal of Agricultural Economics, 81, 287–304.
43.Katz, R. W., G. S. Brush, and M. B. Parlange, 2005, “Statistics of extremes: modeling ecological disturbances,” Ecology, 86(5), 1124-1134.
44.Katz, R.W., 2002, “Stochastic Modeling of Hurricane Damage,” Journal of Applied Meteorology, 41, 754-762.
45.Klugman, S., H. Panjer, and G. Willmot, Loss Models, From Data to Decisions, Wiley, New York, 2004.
46.Kremer, E., 1994, “More on the Probable Maximum Loss,” Blatter der Deutschen Gesellschaft fur Versicherungsmathematik, 319-25.
47.Lai, L. H., 2009, “Risk estimate of rice damaged due to flood,” Nonlinear Analysis: Real World Applications. (In press)
48.Lai L. H., and P. H. Wu, 2009, “Estimating the probable maximum loss and Generalized Pareto Distribution: The Case of Rice Damaged by Typhoons,” The Empirical Economics Letters. (Accepted forthcoming)
49.Lai, L. H., and P. H. Wu, 2008, “Estimating the threshold value and loss distribution: Rice damaged by typhoons in Taiwan,” African Journal of Agricultural Research, 3(12), 818-824.
50.Lansigan, F. P., W. L. De los Santos, and J. O. Coladilla, 2000, “Agronomic impacts of climate variability on rice production in the Philippines,” Agriculture, Ecosystems & Environment, 82(1-3), 129-137.
51.Larsson, H., 2005, “A crop loss model and economic thresholds for the grain aphid, Sitobion avenae (F.), in winter wheat in southern Sweden,” Crop Protection, 24(5), 397-405.
52.Leadbetter, M. R., G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983.
53.Levi, C., and C. Partrat, 1991, “Statistical analysis of natural events in the United States,” ASTIN Bulletin, 21(2), 239-276.
54.Li, Y., W. Ye, M. Wang, and X. Yan, 2009, “Climate change and drought: a risk assessment of crop-yield impacts,” Climatic Change, 39, 31-46.
55.Lin, C. Y., 2001, “An Economic Analysis of Alternative Rice Insurance Policies in Taiwan,” Taiwanese Agricultural Economic Review, 6(2), 235-253. (In Chinese)
56.Lin, H. S., 2007, “Agrometeorological Disasters Occurred on Vegetables in Taiwan and Its Responsive Strategies,” Crop, Environment & Bioinformatics, 4(1), 23-34.new window
57.Longin, F. M, 2000, “From value at risk to stress testing: The extreme value approach,” Journal of Banking & Finance, 24, 1097-1130.
58.Luo, Y., P. S. Teng, N. G. Fabellar, and D. O. TeBeest, 1998, “Risk analysis of yield losses caused by rice leaf blast associated with temperature changes above and below for five Asian countries,” Agriculture, Ecosystems & Environment, 68(3), 197-205.
59.McNeil, A. J., and R. Frey, 2000, “Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach,” Journal of Empirical Finance, 7(3-4), 271–300.
60.McNeil, A. J., 1997, “Estimating the tails of loss severity distributions using extreme value theory,” ASTIN Bulletin, 27(1), 117-137.new window
61.McNeil, A. J., and T. Saladin, 1997, “The peaks over thresholds method for estimating high quantiles of loss distributions,” Proceedings of 28th International ASTIN Colloquium.
62.Muralidharan, K., and I. C. Pasalu, 2006, “Assessment of crop losses in rice ecosystems due to stem borer damage (Lepidoptera: Pyralidae),” Crop Protection, 25, 409-417.
63.Nelson, C. H., and P. V. Preckel, 1989, “The conditional Beta distribution as a stochastic production function,” American Journal of Agricultural Economics, 71, 370-78.
64.Papush, D. E., G. S. Patrick, and F. Podgaits, 2001, “Approximations of the Aggregate Loss Distribution,” Casualty Actuarial Society Forum Casualty Actuarial Society, Winter, 175-186.
65.Perignon, C., Z. Y. Deng, Z. J. Wang, 2008, “Do banks overstate their Value-at-Risk?” Journal of Banking & Finance, 32, 783–794.
66.Pickands, J. I., 1975, “Statistical inference using extreme value order statistics,” Annals of Statistics, 3, 119–131.
67.Pritsker, M., 1997, “Evaluating value at risk methodologies,” Journal of Financial Services Research, 12(2), 201–242.
68.Promislow, S. D., Fundamentals of Actuarial Mathematics, John Wiley & Sons, New York, 2006.
69.Reiss, R. D., and M. Thomas, Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields, Birkh¨auser Verlag, Basel, 1997.
70.Rockafellar, R. T., S. Uryasev, 2002, “Conditional value-at-risk for general loss distributions,” Journal of Banking & Finance, 26, 1443–1471.
71.Rootzen, H., and N. Tajvidi, 1997, “Extreme value statistics and windstorm losses: A case study,” Scandinavian Actuarial Journal, 1, 70–94.new window
72.Rosenberg, J. V., and T. Schuermann, 2005, “A general approach to integrated risk management with skewed, fat-tailed risks,” Journal of Financial Economics, 79, 569-614.
73.Rosenzweig, C., F. Tubiello, R. Goldberg, E. Mills, and J. Bloomfield, 2002, “Increased crop damage in the U.S. from excess precipitation under climate change,” Global Environmental Change, 12(3), 197-202.
74.Seal, H. L., 1977, “Approximations to risk theory''s F(x,t) by means of the gamma distribution,” ASTIN Bulletin, 9, 213-218.
75.Sirakumar, M. V. K., R. P. Motha, and H. P. Das, Natural disasters and extreme events in agriculture, Springer, New York, 2005.
76.Smith, D. L., J. J. Almaraz, 2004, “Climate change and crop production: contributions, impacts, and adaptations,” Canadian Journal of Plant Pathology, 26(3), 253-266.
77.Smolka, A., 2006, “Natural disaster and the challenge of extreme events: risk management from an insurance perspective,” Philosophical Transactions of the Royal Society, 364, 2147-2165.
78.Su, W. P., H. L. Yang, 1997, “Analysis of premiums of rice crop insurance in Taiwan,” Taiwan Economy Monthly, 247, 81-98. (In Chinese)
79.Sundt, B., 1982, “Asymptotic behavior of compound distributions and Stop-Loss premiums,” AST1N Bulletin, 13(2), 89-98.
80.Tasche, D., 2002, “Expected shortfall and beyond,” Journal of Banking & Finance, 26, 1519–1533.
81.Tsao, C. W., 2008, “Introduction to Taiwan’s Agricultural Natural Disaster Assistance Regulation Amendment,” Agriculture Policy & Review, 192, 12-18. (In Chinese)
82.Tsvetsinskaya, E. A., L. O. Mearns, T. Mavromatis, W. Gao, L. Mcdaniel, and M. W. Downton, 2003, “The effect of spatial scale of climate change scenarios on simulated maize, winter wheat, and rice production in the southeastern united states,” Climate Change, 60, 37-71.
83.Tung, S. C., 2001, “The Feasibility Study of the Establishment of Crop Insurance in Taiwan--the Application of Actuarial Break-Even Model,” Master Dissertation, Department of Risk and Insurance, National Kaohsiung First University Science and Technology. (In Chinese)
84.Walshaw, D., and C. W. Anderson, 2000, “A model for extreme wind gusts,” Applied Statistics, 49(4), 499-508.
85.Wang, H., and H. Zhang, 2003, “On the Possibility of Private Crop Insurance Market: A Spatial Statistics Approach,” Journal of Risk and Insurance, 70, 111-124.
86.Wilkinson, M. E., 1982, “Estimating probable maximum loss with order statistics,” Proceedings of the Casualty Actuarial Society, 69, 195-209.
87.Wu, P. I., H. Y. Shen, J., and L. Liou, 2005, “Policy Design and Simulation Analysis for Rice Crop Revenue Insurance Under WTO Agreement,” Proceedings of 2005 KAEA-REST International Conference, Taipei. (In Chinese)
88.Wu, T. C., 2008, “Introduction to Taiwan’s agricultural natural disaster assistance program” National Policy Foundation Commentary, Economy and Technology, NO. 097-043. (In Chinese)
89.Xtreme Group, Xtremes Online Help, Version 3.0., Xtreme Group, Siegen, 2001.
90.Yamai, Y., T. Yoshiba, 2005, “Value-at-risk versus expected shortfall: A practical perspective,” Journal of Banking & Finance, 29, 997–1015.
91.Yamamoto, H., and K. Iwaya, 2006, “Salt wind damage on rice by typhoon 0415 (MEGI) on the Sea of Japan coastal region of Tohoku and Hokuriku districts,” Japanese Journal of Crop Science, 75(1), 73-81.new window
 
 
 
 
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