過去有相當多的文獻針對解約率建立模型，但由於資料取得之困難，鮮少文獻針對不同保單年度之解約率進行分析，本研究將以台灣壽險業資料分析不同保單年度之解約率行為，期望能找出解約率之期限結構，提供壽險業者訂價或風險管理之參考依據。 　　本研究使用台灣壽險業1987年至2011年間之生死合險及終身壽險資料，透過資料分析顯示兩險種之解約率關聯性不大，且應將繳別分為三類進行分析，分別為不分繳別、月繳及年繳和半年繳及季繳三類，針對各保單年度進行主成分分析，結果顯示皆需6至8個主成分方可達到90%之解釋力，並透過ARMA模型檢驗選定之主成分與總體經濟變數間之關聯性，進而觀察是否符合利率假說及緊急資金假說，最後透過VAR模型或ARMA模型模擬總體經濟變數和各主成分之分數，並利用主成分分析之結果將主成分分數轉換回保單年度變數，完成各保單年度解約率之模擬，建構出台灣壽險業解約率之期限結構。

Two measures of air temperature trends across southern Yukon and northern British Columbia were modelled based on measurements from 83 monitoring sites across seven areas, operating for up to 14 years. Both mean monthly air temperature (MMAT) and freezing and thawing degree days (FDD and TDD, respectively) were modelled across this area (59 °N to 64.5 °N) at elevations ranging from 330-1480 m asl. Lapse rates in this region show inversions in the winter months (November - March) varying in inversion strength and length in relation to degree of continentality. The spatial and elevation range of these sites allowed for regional lapse rate modelling at the monthly scale for MMAT and at the annual scale for FDD and TDD. Lapse rates below treeline were found to be correlated (p < 0.1) with degree of continentality in the colder months (November - April) and August. In these months, lapse rates were modelled using kriging trend surfaces. In months where degree of continentality was not found to have a significant impact on lapse rates (p > 0.1) (May - October, excluding August), an average lapse rate calculated from the seven study regions was used across the study region. A combination of lapse rate trend surfaces, elevation, and temperatures at sea level were used to model MMAT and F/TDD below treeline. A treeline trend surface was created using a 4th order polynomial, allowing for temperatures at treeline to be determined. MMAT and F/TDD above treeline were calculated using a constant lapse rate of -6 °C/km, elevation, and temperature at treeline. The above and below treeline models were combined to create continuous models of MMAT and F/TDD. Modelled MMAT showed a high degree of homogeneity across the study region in warmer months. Inversions in lapse rates are evident in the colder months, especially December through February, when colder temperatures are easily identified in valley bottoms, increasing to treeline, and decreasing above treeline. Modelled MMAT values were validated using 20 sites across the study region, using both Environment and Climate Change Canada and University of Ottawa sites. The RMSE between modelled and observed MMAT was highest in January (4.4 °C) and lowest in June (0.7 °C). Sites below treeline showed a stronger relationship between modelled and observed values than sites above treeline. Edge effects of the model were evident in the northeast of the study region as well as in the ice fields in the southwest along the Alaska border. The new MMAT maps can be used to help understand species range change, underlying permafrost conditions, and climate patterns over time. FDD values were found to be highly influenced by both degree of continentality as well as latitude, whereas TDD values were mainly dependent on elevation, with degree of continentality and latitude being lesser influences. FDD and TDD were validated using the same 20 sites across the study region, with FDD showing a larger RMSE (368 degree days) between modelled and observed values than TDD (150 degree days). TDD modelling performed better on average, with a lower average absolute difference (254 degree days) between modelled and observed values at the validation sites than FDD modelling (947 degree days). The models of FDD and TDD represent a component of temperature at top of permafrost (TTOP) modelling for future studies. Two mean annual air temperature (MAAT) maps were created, one calculated from the MMAT models, and the other from the F/TDD models. Most of the study region showed negative MAAT, mainly between -6 °C and 0 °C for both methods. The average MAAT calculated from FDD and TDD values was -2.4 ºC, whereas the average MAAT calculated from MMAT values was -2.8 ºC. Models of MAAT were found to be slightly warmer than in previous studies, potentially indicating warming temperature trends.

Thesis (PhD (Mechanical and Mechatronic Engineering))-- University of Stellenbosch, 2007. / ENGLISH ABSTRACT: The dissertation builds on previous research (Pretorius, 2004) and investigates the optimization and control of a large-scale solar chimney power plant. Performance results are based on a reference location near Sishen in South Africa and a so-called reference solar chimney power plant, with a 5000 m collector diameter and a 1000 m high, 210 m diameter chimney. The numerical simulation model is refined and used to perform a sensitivity analysis on the most prominent operating and technical plant specifications. Thermo-economically optimal plant configurations are established from simulation results and calculations according to an approximate plant cost model. The effects of ambient wind, temperature lapse rates and nocturnal temperature inversions on plant performance are examined. Various new technologies are investigated for the purpose of controlling plant output according to specific demand patterns. The incorporation of vegetation under the collector roof of the plant and the influence thereof on plant performance is also explored. Results indicate that, through the modification of the collector roof reflectance, collector roof emissivity, ground surface absorptivity or ground surface emissivity, major improvements on plant performance are possible. Introducing thermal insulation or double glazing of the collector roof also facilitates substantial enhancements on plant yield. Simulations predict a notable sensitivity to the ground surface absorptivity value, while variable atmospheric temperature lapse rates and windy ambient conditions may impair plant performance significantly. Furthermore, sand is found to be unsuitable as plant ground type and thermoeconomically optimal solar chimney plant dimensions are determined to be generally larger than plant dimensions employed in previous studies. Good dynamic control of solar chimney power output is established, suggesting that a solar chimney power plant can be implemented as a base or peak load electricity generating facility. Lastly, results predict that vegetation, when provided with sufficient water, will be able to survive under the collector roof but the inclusion of vegetation will however cause major reductions in plant performance. / AFRIKAANSE OPSOMMING: Die proefskrif bou op vorige navorsing (Pretorius, 2004) en ondersoek die optimering en beheer van 'n grootskaalse sonskoorsteen-kragstasie. Uitsetresultate word baseer op 'n verwysingsligging naby Sishen in Suid-Afrika en 'n sogenaamde verwysingskragstasie, met 'n kollektor deursnee van 5000 m en 'n 1000 m hoë, 210 m deursnee skoorsteen. Die numeriese rekenaarmodel is verbeter en gebruik vir die uitvoering van 'n sensitiwiteits-analise op die belangrikste bedryfs- en tegniese kragstasie spesifikasies. Termo-ekonomiese optimale aanlegkonfigurasies is bepaal volgens die uitsetresultate van die rekenaarmodel en benaderde aanleg-kosteberekeninge volgens 'n eenvoudige kostemodel. Die invloed van wind, atmosferiese temperatuur gradiënte en nagtelike temperatuur inversies op kragstasie uitset word beskou. Verskeie nuwe tegnologië word ondersoek met die doel om aanleg uitset te kan beheer volgens spesifieke elektrisiteit aanvraagspatrone. Die inkorporasie van plantegroei onder die kollektordak, en die invloed daarvan op kragstasie uitset, word ook beskou. Bevindings dui aan dat, deur die wysiging van die kollektordak refleksie, kollektordak emissiwiteit, grondoppervlak absorptiwiteit of grondoppervlak emissiwiteit, groot verbeterings op aanleg uitset moontlik is. Die implementering van termiese isolasie of 'n dubbelglaslaag vir die kollektordak veroorsaak ook 'n beduidende verheffing in kragstasie uitset. Simulasies voorspel 'n merkbare sensitiwiteit teenoor die grondoppervlak absorptiwiteitswaarde, terwyl veranderlike atmosferiese temperatuur daaltempos en winderige omgewingstoestande aanleg uitset beduidend mag belemmer. Verder is bevind dat sand ongeskik is as aanleg grond tipe en dat termo-ekonomiese optimale sonskoorsteen-kragstasie dimensies in die algemeen groter is as die aanvaarde aanlegdimensies van vorige studies. Goeie dinamiese beheer van sonskoorsteen-kragstasie uitset is bevestig, wat suggereer dat die sonskoorsteenkragstasie as 'n basis of pieklas elektrisiteitopwekkings-aanleg ingespan kan word. Ten laaste voorspel resultate dat plantegroei, mits dit voorsien word van genoegsame water, sal kan oorleef onder die kollektordak maar dat die inkorporasie van plantegroei die aanleg uitset beduidend sal benadeel. / Sponsored by the Centre for Renewable and Sustainable Energy Studies

一般而言，壽險公司會在保險契約生效前就支付保單相關之費用，例如核保與承保之成本，並且公司會預期未來保險期間內可以填補上述費用；但若保戶於保險期間內早期解約或是解約情形嚴重，將使壽險公司難達到損益兩平之目標而招受損失，影響公司預期盈收，進而增加公司資金調度上之困難。因此，對於長期穩健經營之壽險公司而言，瞭解各保險解約率變動情形對於公司之財務規劃相當重要，以期降低危害公司之風險。 本文期望藉由台灣保險事業發展中心之實證資料蒐集與相關分析，探討影響台灣壽險業生死合險及不還本終身壽險解約之因素以及其解約率之特性，進而建立與利差及保單年度相關之解約率模型，以期能準確地估計台灣壽險公司生死合險解約率與不還本終身壽險解約率。除此之外，本研究將所建構之解約率模型應用於公司未來現金流量分析，以蒙地卡羅法模擬各險種保單準備金之分配，瞭解各種解約率假設對於公司未來現金流量之影響，進而瞭解解約率參數假設對於準備金風險之評估扮演重要角色。 / In general, the life insurance companies would pay the expenses with respect to the insurance policies before the validity of insurance contracts such as underwriting and insuring costs. If the policyholders are early-surrendered or over-surrendered during the policy period, then it will make the insurance companies hard to achieve their break-even goal and result in affecting the companies’ surplus as well as management of their capital. Thus, for the long-term and stable life insurance companies, it is extremely important to understand the changes of lapse rate in order to reduce the financial risk damage before making any financial decisions. In this article, we expect to focus on the causes and the features of lapse rate changes by collecting and analyzing the empirical data of endowment and whole life insurance in Taiwan from Taiwan Insurance Institute. Based on our analysis, we could build the lapse rate model concerning the relation between the lapse rate and interest rate difference or policy year for estimating the endowment lapse rate and whole life insurance lapse rate accurately. Moreover, we apply the lapse rate model to company’s cash flow analysis. We employ the Monte Carlo simulation to simulate the policy reserve distribution, and we find out that the lapse rate assumption plays an important role in the policy reserve evaluation.

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中文摘要 在本文中，我們依據模擬的風險因子變動，包括死亡率風險，利率風險，解約率風險以及模型的參數風險，來估計第一個保單年度的期末責任準備金之涉險值 (Value at Risk)。本文中，雖僅計算生死合險保單的準備金之涉險值，但是本文所提供的方法以及計算過程可以很容易的應用到其它險種，甚至配合資產面的考量來計算保險公司盈餘(Surplus)的涉險值，進而作為清償能力的監測系統。 本文的特點包括下列幾項：第一，本文提供了一個不同於傳統短期間(Short Horizon)的涉險值計算方式，來估計壽險商品的保單責任準備金(Policy Reserve)的涉險值。第二，本文利用生命表來估計死亡率風險所造成的涉險值。第三，我們利用隨機利率模型來捕捉隨機利率對於責任準備金涉險值的影響。第四，我們考慮解約率對於責任準備金涉險值的影響，值得注意的是，在我們的解約率模型中，引入的利率對於解約率的影響。第五，本文亦考慮風險因子模型當中的參數風險對於涉險值的影響。最後，我們利用無母數方法計算出涉險值的信賴區間，而信賴區間的估計在模擬過程當中尤其重要，因為它可以用來決定模擬次數的多寡。 本文包含六節：第一節為導論。第二節為計算死亡率風險的責任準備金涉險值。第三節是計算加上利率風險後責任準備金涉險值的變化。第四節則為加上解約率後對涉險值的影響。第五節為計算涉險值的信賴區間。第六節是我們的結論以及後續研究的方向探討。 本文包含六節：第一節為導論。第二節為計算死亡率風險的責任準備金涉險值。第三節是計算加上利率風險後責任準備金涉險值的變化。第四節則為加上解約率後對涉險值的影響。第五節為計算涉險值的信賴區間。第六節是我們的結論以及後續研究的方向探討。 / ABSTRACT In this paper, we estimate the VAR of life insurer's terminal reserve of the first policy year by the simulated risk factors, including mortality risk, interest rate risk, lapse rate risk, and estimation risks, of future twenty years. We found that the difference between the VAR under the mortality risk and the interest rate risk is very large because interest rate is a stochastic process but not mortality rate. Thus, the dispersion of interest rate is more then mortality rate. In addition, the VAR will reduce a lot after adding the impact of lapses because the duration of the reserve reduced. If we neglect the impact of lapses to VAR, we will overestimate the VAR significantly. The features of this paper are as follows. First, we provide an approach to measure the VAR of a life insurer's reserve, and it is rather different from traditional VAR with short horizons. Second, we use mortality table to estimate the VAR of a life insurer's reserve. Third, we use stochastic interest rate model to capture the effect of random interest rate to the VAR of a life insurer's reserve. Fourth, we relate the future cash outflows to interest rate and produce a reasonable estimator of VAR. Fifth, we consider the effect of estimation errors to the VAR of a life insurer's reserve. Last, we calculate the confidence interval of the VAR estimates of the policy reserves. This paper consists of six sections. The first section is an introduction. In the second section, we present the method used to estimate the variance of the mortality rate and then estimate the VAR of reserves from these variances. In the third section, we explore how to use stochastic interest rate model to estimate the reserve's VAR and the VAR associated with the parameter risk of the interest rate model. In the fourth section, we analyze the contribution of the lapse rate risk and the parameter risk of the lapse rate model to the reserve's VAR. We also analyze the relative significance of the interest rate risk, the lapse rate risk, and the mortality rate risk in terms of their marginal contributions to the VAR of an insurer's reserves in this section. In the fifth section, we calculate the confidence intervals of the VAR estimates discussed in the previous sections. The last section is the conclusion section containing our conclusions and discussions about potential future researches.