The situation that China's pensions cannot cover the expenditure is becoming more and more serious. On the one hand, it is to increase the rate of return of enterprise annuities. On the other hand, it is to increase the participation rate of enterprise annuities. In order to improve the participation rate of enterprise annuity, it is of great significance to solve the problem of insufficient funds of enterprise annuity from the aspect of supply. Based on this, this dissertation conducts detailed research, focusing on the impact of relevant factors on the participation rate of enterprise annuity from the enterprise level and the individual level. After making a detailed overview of the situation of domestic enterprise annuity, this dissertation analyzes the influencing factors of the participation rate of enterprise annuity of China based on the latest nationally representative micro data CHIP 2018. The analysis uses the "bivariate Probit model", that is, the enterprise level and the individual level, employing 0-1 bivariate as the dependent variables and employee income, employee education, employee gender, enterprise income as independent variables. The analysis also includes other control variables. The empirical evidence found that employee income, employee education, and employee gender have impacts on employee participation in enterprise annuity; enterprise ownership, company income, and the industry in which the company is located have impacts on whether the enterprise establishes an enterprise annuity plan. In addition, there are differences in the state-owned system and private system and industry differences on the establishment of enterprise annuity plans. Finally, this dissertation gives relevant policy suggestions that may provide some theoretical guidance for increasing the participation rate of enterprise annuity.Key words: Enterprise annuity; Participation rate; Bivariate Probit model; Policy suggestions. / Business Administration/Interdisciplinary

This thesis addresses the absence of explicit pricing formulae and the complexity of proposed models (incomplete markets framework) in the area of mortality risk management requiring the application of advanced techniques from the realm of Financial Mathematics and Actuarial Science. In fact, this is a multi-essay dissertation contributing in the direction of designing and pricing mortality-linked derivatives and offering the state of art solutions to manage longevity risk. The first essay investigates the valuation of Catastrophic Mortality Bonds and, in particular, the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of assets. This bond was the first Catastrophic Mortality Bond to be launched in the market and encapsulates the behaviour of a well-defined mortality index to generate payoffs for bondholders. Pricing this type of bond is a challenging task and no closed form solution exists in the literature. In my approach, we adapt the payoff of such a bond in terms of the payoff of an Asian put option and present a new methodology to derive model-independent bounds for catastrophic mortality bonds by exploiting the theory of comonotonicity. While managing catastrophic mortality risk is an upheaval task for insurers and re-insurers, the insurance industry is facing an even bigger challenge - the challenge of coping up with increased life expectancy. The recent years have witnessed unprecedented changes in mortality rate. As a result academicians and practitioners have started treating mortality in a stochastic manner. Moreover, the assumption of independence between mortality and interest rate has now been replaced by the observation that there is indeed a correlation between the two rates. Therefore, my second essay studies valuation of Guaranteed Annuity Options (GAOs) under the most generalized modeling framework where both interest rate and mortality risk are stochastic and correlated. Pricing these types of options in the correlated environment is an arduous task and a closed form solution is non-existent. In my approach, I employ the use of doubly stochastic stopping times to incorporate the randomness about the time of death and employ a suitable change of measure to facilitate the valuation of survival benefit, there by adapting the payoff of the GAO in terms of the payoff of a basket call option. I then derive general price bounds for GAOs by employing the theory of comonotonicity and the Rogers-Shi (Rogers and Shi, 1995) approach. Moreover, I suggest some `model-robust' tight bounds based on the moment generating function (m.g.f.) and characteristic function (c.f.) under the affine set up. The strength of these bounds is their computational speed which makes them indispensable for annuity providers who rely heavily on Monte Carlo simulations to calculate the fair market value of Guaranteed Annuity Options. In fact, sans Monte Carlo, the academic literature does not offer any solution for the pricing of the GAOs. I illustrate the performance of the bounds for a variety of affine processes governing the evolution of mortality and the interest rate by comparing them with the benchmark Monte Carlo estimates. Through my work, I have been able to express the payoffs of two well known modern mortality products in terms of payoffs of financial derivatives, there by filling the gaps in the literature and offering state of art techniques for pricing of these sophisticated instruments.

Title: Modelling Dependent Lives Author: Eva Pavčová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we model the dependence between the remaining lifetimes of a husband and wife using a specific Markov model. We examined the impact of the dependence on the net single premium using the specific Markov model that captures the long-term dependence between lifetimes of the two considered lives. Using this model we have calculated 10-year joint-life annuity due and 10-year last-survivor annuity due considering the age rage (37, 80) in case of dependence and also independence of the two considered lives. The calculations were based on the dataset related to the Czech population in 2015. The impact of the dependence between the remaining lifetimes of the husband and wife was found to be not significant. Keywords: positive quadrant depedence, multiple life insurance premiums, depen- dent lifetimes, joint-life annuity, last-survivor annuity, joint-life and last-survivor models

Då det finns planer på att ersätta det befintliga reningsverket i Kalmar inom en överskådlig framtid och nya krav om nödförsörjning av el har kommit från MSB, undersöktes möjligheten att använda den biogas som skulle komma att produceras på det nya reningsverket inom den egna verksamheten, istället för att som i dagsläget säljas. I denna studie undersöktes lönsamheten i att antigen investera i en biogasdriven generator som i normalfall ger en besparing i el och fjärrvärme och kan leverera reservkraft vid spänningsbortfall på nätet, eller försäljning av biogasen och inköp av ett dieseldrivet reservkraftverk.  Kostnadsförslag för biogasdrivna generatorer och reservkraftverk togs in. I denna ingick även service och komponenter för att kunna använda biogasen som bränsle. Utav kostnadsförslagen gjordes en LCC. Besparing av el och fjärrvärme samt förtjänst av försäljning av biogasen ställdes i relation mot varandra. Arbetet konkluderar att, baserat på de uträkningar som gjordes, en ottomotor är det mest lönsamma för att generera el och värme för internt bruk. / Because of the plans to replace the old sewage treatment plant in Kalmar, which has come to the end of its life cycle, and due to new requirements of emergency supply from SCCA (Swedish Civil Contingencies Agency), the possibility of using the biogas on the plant itself was evaluated. In this study, the profitability of two alternatives was evaluated. To invest in a biogas powered generator to produce electric power and heat, which would create savings in purchased electricity and district heating and work as an emergency generator, or to continue selling the biogas and invest in a diesel-powered emergency generator. Cost estimates of biogas powered generators and the equipment needed for using the biogas as fuel was required from dealers and manufacturers. The cost estimates were then compiled in a LCC. The calculated savings and the income from selling the biogas was then added to the LCC, the alternatives was then compared to each other. The study concludes that the most profitable alternative, based on the calculations, is to invest in a biogas powered generator and use the electricity and waste heat on the sewage plant.

躉繳遞延年金在美國已成最受歡迎的壽險商品，究其原因，實是該商品具 備庇護的茲息收益、特惠的稅賦措施、投資的安全性及多樣化的提款選擇 權等特色。在美國常見的年金商品選擇權，如：豁免條款、免費部份提款 、無部份提款之加給、市場價值調整、兩層利率年金、提前年金化、年金 化前之死亡給付等等，其用意是在保單累積期中給予保戶較自由資金運用 的權利，藉此吸引顧客並與銀行之儲蓄商品來競爭。在準備金提存方面， 其現金價值累積是與市場利率有密切關係，性質迴異於以往的壽險型年金 商品，一般壽險準備金方法無法運用於該類商品，故美國ＮＡＩＣ於１９ ７６年提出監理官制年金準備金評價方法（ＣＡＲＶＭ），以作為該類商 品責任準備金之最低提存標準。未來國內年金發展方向應會朝向美國模式 ，以及早規劃適當的年金準備金方法。 Discussing the liability reserveof annuity from American Single Premium deferred Annuity(SPDA)

A guaranteed minimum income benefit (GMIB) is a long-dated option that can be embedded in a deferred variable annuity. The GMIB is attractive because, for policyholders who plan to annuitize, it offers protection against poor market performance during the accumulation phase, and adverse interest rate experience at annuitization. The GMIB also provides an upside equity guarantee that resembles the benefit provided by a lookback option. We price the GMIB, and determine the fair fee rate that should be charged. Due to the long dated nature of the option, conventional hedging methods, such as delta hedging, will only be partially successful. Therefore, we are motivated to find alternative hedging methods which are practicable for long-dated options. First, we measure the effectiveness of static hedging strategies for the GMIB. Static hedging portfolios are constructed based on minimizing the Conditional Tail Expectation of the hedging loss distribution, or minimizing the mean squared hedging loss. Next, we measure the performance of semi-static hedging strategies for the GMIB. We present a practical method for testing semi-static strategies applied to long term options, which employs nested Monte Carlo simulations and standard optimization methods. The semi-static strategies involve periodically rebalancing the hedging portfolio at certain time intervals during the accumulation phase, such that, at the option maturity date, the hedging portfolio payoff is equal to or exceeds the option value, subject to an acceptable level of risk. While we focus on the GMIB as a case study, the methods we utilize are extendable to other types of long-dated options with similar features.

為進一步保障勞工老年退休後經濟狀況無虞，維持其原本生活水平，行政院會於2011年12月29日通過《勞工退休金條例》修正草案，放寬企業開辦年金保險條件，企業規模在200人以上者，只要經工會或勞資會議同意，即可開辦企業年金保險，而勞工也可審視其收益狀況，選擇是否將個人退休金專戶轉換為企業年金保險。此項立法通過後，可望帶動壽險公司勞退自提部分企業年金保險商品的銷售商機。 站在勞工的角度來看，任職公司為職工規劃企業年金保險，可以讓員工提早為退休金做儲蓄，更專注於工作做努力。 從政府的角度觀察，為國內勞工做好規劃及監督與把關，更加健全、完善與更多選擇的退休金商品與制度，能給予勞工一個無憂無慮的退休生活，相對的能節省更多可能的社會福利支出，將政府資源投入國家基礎建設與經濟發展中。 站在壽險公司的方向研究，企業退休金市場的經營一直都是壽險公司所高度關注的一個區塊，只要提供適合的商品及規劃，企業為勞工、勞工為自己所提存的保費收入，是每月都會有穩定的現金流入，有利於壽險業做長期的投資規劃，再者透過企業年金保險制度的推廣，能接觸到更多的客戶與更加深入了解客戶的需求，便於設計出市場接受度高的商品，有利提供壽險公司的經營與投資績效。 最後從企業經營面來規劃，實施企業年金保險制度，能替員工提供一個更長久的退休計畫，為企業規劃一個更完善的員工獎勵制度與留才計畫；員工是企業最重要的資產，若未針對企業中的“人”此項有形資產加以運用，企業將不會產生任何無形的超額利益，本文希望藉由對企業年金保險制度之分析與介紹，期有助於國內壽險業發展企業年金保險與企業參酌實施企業年金保險制度之意願研究之參考。 / To have labors adapt to life after retirement, the Executive Yuan approved the Amendment of the Labor Pension Act on December 29, 2011. From the view of labors, it allows employees to start saving into pension ahead of time and focus more on work if the enterprise that one works for setting out an enterprise annuity insurance plan for its employees. From the government’s point of view, a good plan with constant monitoring and checking on makes a more complete pension funds system, which provides laborers with a better life after retirement. For insurance companies, as long as the insurance company provides suitable product and plan, the premium collected from what enterprises invested for employees and labour’ self-contribution will be stable cash flow on monthly basis, which is beneficial for insurance company to draw a long time investment plan. Finally, in terms of enterprise management, to carry out enterprise annuity insurance will provide employees with a retirement plan with long-term influence and will help to establish a complete reward system and a plan for retaining talent. Through the analysis and introduction of the enterprise annuity insurance in this article, it provides some suggestions for local insurance companies when it comes to develop the enterprise annuity insurance, and also some references for enterprises that are willing to put enterprise annuity insurance system into practice.

A guaranteed minimum income benefit (GMIB) is a long-dated option that can be embedded in a deferred variable annuity. The GMIB is attractive because, for policyholders who plan to annuitize, it offers protection against poor market performance during the accumulation phase, and adverse interest rate experience at annuitization. The GMIB also provides an upside equity guarantee that resembles the benefit provided by a lookback option. We price the GMIB, and determine the fair fee rate that should be charged. Due to the long dated nature of the option, conventional hedging methods, such as delta hedging, will only be partially successful. Therefore, we are motivated to find alternative hedging methods which are practicable for long-dated options. First, we measure the effectiveness of static hedging strategies for the GMIB. Static hedging portfolios are constructed based on minimizing the Conditional Tail Expectation of the hedging loss distribution, or minimizing the mean squared hedging loss. Next, we measure the performance of semi-static hedging strategies for the GMIB. We present a practical method for testing semi-static strategies applied to long term options, which employs nested Monte Carlo simulations and standard optimization methods. The semi-static strategies involve periodically rebalancing the hedging portfolio at certain time intervals during the accumulation phase, such that, at the option maturity date, the hedging portfolio payoff is equal to or exceeds the option value, subject to an acceptable level of risk. While we focus on the GMIB as a case study, the methods we utilize are extendable to other types of long-dated options with similar features.

台灣人口結構老化的趨勢，老人漸漸變成另一種社會不受重視的邊緣人。近年來，由於科技神速發展，職場人員替換週期愈來愈短，許多仍健壯的授薪階級，在智慧與經驗方面雖臻成熟，卻不得不被迫從職場上退下來。最近兩三年來，全球資本主義整體化的併購行為以及中國大陸整體市場崛起連帶引響台灣產業經濟蕭條，更是快速增加了淘汰職場的人數，對於大部分需要依賴勞保及公司退休金制度的勞工階層而言，退休金嚴重不足的情況，更是令人焦慮沮喪。 主管機關為因應社會變遷趨勢，於2000年陸續起開放利率變動型年金與變額年金保險商品於市場銷售，為老年化人口之財務規劃打開另一扇門，年金商品以及投資型保險之觀念架構，為國內消費者提供了多元化保險商品的選擇，化解保險公司利差損的營運壓力，提供創新營運的契機，同時也為壽險從業人員開闢了專業的「全方位金融理財顧問」生涯規劃。 由於投資型保險商品具備保戶可自行執行帳戶價值投資策略之特性，對消費者而言帳戶價值相對於傳統壽險有更大的想像空間，年金型商品由初期著重於銀行定存利率連結概念之利率變動型年金發展至變額年金，兩類商品不約而同的取代了傳統壽險及儲蓄險，對於壽險公司長期經營而言也具有消弭了利差損的風險之營運價值，使得短短的6年之間(2000年-2006年) 傳統壽險，意外險，醫療險之首年度保費佔有率逐年降至40%(中華民國人壽保險公會保費速報 2006.07)。 而不論是投資型保險或年金型保險，在市場之行銷活動均強調資產累積與退休規劃，而在台灣市場兩類主力銷售商品亦存在重疊特質，如變動不保證利率之帳戶價值，帳戶價值提領之彈性，長期運用的理財工具，可單筆大額資金購買亦可分期繳納等特質，使得商品設計多樣化，行政費用收取方式各有不同，行銷訴求則是推陳出新，對消費者而言更不易辨析商品之費用、價格、功能之間所存在價值差異，本研究希望對變額壽險與變額年金兩種商品從消費者需求、商品特性價格與費用等三方面分析此兩種商品在退休規劃之優劣比較。

台灣和世界一樣，人口持續老化，此外台灣在2011年是世界出生率最低的國家，同時在政府財政不斷赤字下，更使政府對公立教師所辦理的第一層社會保險退休年金、第二層對公教所辦理的退休職業年金，陷入前所未見的財務困難，各種精算報告明顯指出，未來十到二十年間，公教退休基金破產，指日可待，因此公教人員退休金制度等的改革浪潮，風起雲湧。 老年人退休金的主要需求來自於：一、一般日常生活需用的費用；二、因為身體退化關係，可能產生的醫療或長期照顧的費用；三、優渥生活品質額外產生的費用。一般民眾包括老師在計算退休金需求時，大多設想到第一項，最多還會設想到第三項。少有人設想到第二項，因為造成退休金需求低估。本研究在個案研究上，對一、二、三項都有著墨。 本研究探討公立中學教師的退休金規劃中，探討商業年金保險對其幫助。主要分為二類族群，一種是擁有退休撫卹制度舊制與新制混合的待退教師；另一種是純粹擁有新制的教師。首先就退休時所需的生活費用與探討政府能給予的退休年金改革前的狀況與改革後的狀況，加上本身自行理財的資產計算退休不足度。再依不同族群，給予商業年金保險的資產配置比例的建議，並討論其規劃前與規劃後的效益差別，進而闡述商業年金保險可保障長壽風險的不可取代性。 本研究做出以下結論：一、若想要規避長壽風險，那就需要年金保險、二、未來政府公教退休年金改革方向，給付只會更少，不會更多；三、商業年金保險和其他資產可以互補或替代；四、開放公保年金化，對新制教師有利月領退休金，降低長壽風險有利。