Thesis (MSc)--Stellenbosch University, 2015 / ENGLISH ABSTRACT : Equity-based insurance guarantees also known as unit-linked annuities are annuities with embedded exotic, long-term and path-dependent options which can be categorised into variable and equity indexed annuities, whereby investors participate in the security markets through insurance companies that guarantee them a minimum of their invested premiums. The difference between the financial options and options embedded in equity-based policies is that financial ones are financed by the option buyers’ premiums, whereas options of the equity-based policies are financed by also continuous fees that follow the premium paid first by the policyholders during the life of the contracts. Other important dissimilarities are that equity-based policies do not give the owner the right to sell the contract, and carry not just security market related risk, but also insurance related risks such as the selection rate, behavioural, mortality, others and the systematic longevity. Thus equity-based annuities are much complicated insurance products to precisely value and hedge. For insurance companies to successfully fulfil their promise of eventually returning at least initially invested amount to the policyholders, they have to be able to measure and manage risks within the equity-based policies. So in this thesis, we do fair pricing of the variable and equity indexed annuities, then discuss management of financial market and insurance risks management. / AFRIKAANSE OPSOMMING : Aandeel-gebaseerde versekering waarborg ook bekend as eenheid-gekoppelde annuiteite is eksotiese, langtermyn-en pad-afhanklike opsies wat in veranderlike en gelykheid geindekseer annuiteite, waardeur beleggers neem in die sekuriteit markte deur middel van versekering maatskappye wat waarborg hulle ’n minimum van geklassifiseer kan word hulle belˆe premies. Die verskil tussen die finansi¨ele opsies en opsies is ingesluit in aandele-gebaseerde beleid is dat die finansi¨ele mense is gefinansier deur die opsie kopers se premies, terwyl opsies van die aandele-gebaseerde beleid word deur ook deurlopende fooie wat volg op die premie wat betaal word eers deur die polishouers gefinansier gedurende die lewe van die kontrakte. Ander belangrike verskille is dat aandele-gebaseerde beleid gee nie die eienaar die reg om die kontrak te verkoop, en dra nie net markverwante risiko sekuriteit, maar ook versekering risiko’s, soos die seleksie koers, gedrags, sterftes, ander en die sistematiese langslewendheid. So aandeel-gebaseerde annuiteite baie ingewikkeld versekering produkte om presies waarde en heining. Vir versekeringsmaatskappye suksesvol te vervul hul belofte van uiteindelik ten minste aanvanklik belˆe bedrag terug te keer na die polishouers, hulle moet in staat wees om te meet en te bestuur risiko’s binne die aandeel-gebaseerde beleid. So in hierdie tesis, ons doen billike pryse van die veranderlike en gelykheid geïndekseer annuiteite, bespreek dan die bestuur van finansiele markte en versekering risiko’s bestuur.

We introduce a new insurance instrument allowing retirees to hedge against risk of mortality and risk of default. At retirement, the retiree is allowed to purchase an annuity that provides a defaultable income stream over his lifetime. The time of mortality and time of default are both uncertain, but are accompanied by determined hazard rates. The retiree will make consumption and investment choices throughout his lifetime, which have certain restrictions: the retiree can never enter a bankruptcy state (negative total wealth), and the investment choices are made in a risk-free financial instrument (such as a treasury bill or bond) and a risky instrument (such as commodities or stock). The retiree also makes insurance premium payments which hedge against mortality and default risks simultaneously. This new form of insurance is one which can be implemented by financial institutions as a means for retirees to protect their illiquid assets. In doing so, we calculate the optimal annuity rate a retiree should purchase to maximize his utility of consumption and bequest.Throughout the paper, we develop stochastic control models for a retiree's optimal investment and consumption policies over an uncertain planning horizon in several models which may or may not allow for insurance purchases. We find exact solutions to several models, and apply dynamic programming and the logarithmic transformation to other models to find numerical solutions when constraints are needed. We also analyze the effects of loading on insurance, analyzing the effects of more expensive insurance on the retiree's control policies and value functions. In particular, we will consider the model in which the retiree can purchase life insurance and credit default insurance (in the form of a credit default swap, or CDS) separately to hedge against life events. CDS's do not exist for annuities, but we extend this model by incorporating life insurance and the CDS into a single entity, which can be a viable, and realistic, option to hedge against risk. This model is beneficial in providing a solution to the annuity problem by showing that minimal annuity purchase is optimal.

Essay I: This essay provides an overview of the history of the Swedish pension system. Starting with the implementation of the public pension system in 1913, it outlines the key components of each major pension reform up until today along with a discussion of the main trade-offs and concerns that policy makers have faced. It also describes the historical background of the four largest occupational pension plans in Sweden and the mutual influence between these plans and the public pension system.        Essay II: Despite the fact that the increasing involvement of the private sector in pension provision has brought more flexibility to the pay-out phase of retirement, little is known about the characteristics of those who choose to annuitize their pension wealth and those who do not. I combine unique micro-data from a large Swedish occupational pension plan with rich national administrative data to study the choice between life annuities and fixed-term payouts with a minimum payout length of 5 years for 183,000 retiring white-collar workers. I find that low accumulation of assets is strongly associated with the choice of the 5-year payout. Consistent with individuals selecting payout length based on private information about their mortality prospects, individuals who choose the 5-year payout are in worse health, exhibit higher ex-post mortality rates and have shorter-lived parents than annuitants. Individuals also seem to respond to large, tax-induced changes in annuity prices.            Essay III: This essay estimates the causal effect of postponing retirement on a wide range of health outcomes using Swedish administrative data on cause-specific mortality, hospitalizations and drug prescriptions. Exogenous variation in retirement timing comes from a reform which raised the age at which broad categories of Swedish local government workers were entitled to retire with full pension benefits from 63 to 65. The reform caused a remarkable shift in the retirement distribution of the affected workers, increasing the actual retirement age by more than 4.5 months. Instrumental variable estimation results show no effect of postponing retirement on the overall consumption of health care, nor on the risk of dying early. There is evidence, however, of a reduction in diabetes-related hospitalizations and in the consumption of drugs that treat anxiety. Essay IV (with Per Engström): The consumption based method to estimate underreporting among self-employed, introduced by Pissarides and Weber (1989), is one of the workhorses in the empirical literature on tax evasion/avoidance. We show that failure to account for transitory income fluctuations in current income may overestimate the degree of underreporting by around 40 percent. Previous studies typically use instrumental variable methods to address the issue. In contrast, our access to registry based longitudinal income measures allows a direct approach based on more permanent income measures. This also allows us to evaluate the performance of a list of instruments widely used in the previous literature. Our analysis shows that capital income is the most suitable instrument in our application, while education and housing related measures do not seem to satisfy the exclusion restrictions.

民國94年7月1日開始施行的勞工退休金條例，是政府近年來對勞工退休規劃的重要施政政策，依據此條例規定，員工超過二百人以上的企業，多了企業年金保險的選項可供選擇。而依據第14條第三款規定，勞工得在其每月工資百分之六範圍內，自願另行提繳退休金。勞工自願提繳部份，得自當年度個人綜合所得稅總額中全數扣除。本研究開始之時適逢勞退新制實施之初，並無企業年金中個人相對提撥之實際資料，因此藉分析個人年金保險保戶之屬性及對年金保險消費型態之探討，推論企業年金中選擇自願提繳之個人因素，供各界參考。 本研究整理與回顧國內外相關之職業退休金制度，並探討OECD各國企業年金的運作方式，以及國內年金市場的結構與產品。在實証模型上，則利用線性迴歸模型（OLS），分析影響年金保險保額的原因，並利用間斷性機率模型Probit Model 探討影響傳統型年金保險或投資型年金保險的因素。 / The Labor Pension Act, one of the major policies for the labor retirement planning of the R.O.C. government, was officially put into practice on July 1st, 2005. Based on the regulation of the Act, companies with more than 200 employees will have the Annuity Insurance as alternatives. According to the Article 14 -3 of the Act, a worker may voluntarily contribute per month, up to 6% of his/her monthly wages to his/her pension fund account. The full amount of the voluntary pension contribution made by a worker may be deducted from the worker's taxable income in the year concerned. Therefore, this research intends to analysis between the attributions and consumption behaviors of the employees joining in the policy of the Annuity Insurance, and then generalizes the factors why the workers choose the voluntary pension contribution policy. In this research, I would compare the pension policies used in different countries, look into the ways that the OECD are running their Enterprise Annuity policies, and evaluate the various pension policies. By using the real diagnosis Model, I would use the OLS to analysis the influences over Annuity Insurance Insured value and then use the Probit Model to explore the influences over traditional Annuity Insurance and the Investment Annuity Insurance.

Essay I: This essay provides an overview of the history of the Swedish pension system. Starting with the implementation of the public pension system in 1913, it outlines the key components of each major pension reform up until today along with a discussion of the main trade-offs and concerns that policy makers have faced. It also describes the historical background of the four largest occupational pension plans in Sweden and the mutual influence between these plans and the public pension system.        Essay II: Despite the fact that the increasing involvement of the private sector in pension provision has brought more flexibility to the pay-out phase of retirement, little is known about the characteristics of those who choose to annuitize their pension wealth and those who do not. I combine unique micro-data from a large Swedish occupational pension plan with rich national administrative data to study the choice between life annuities and fixed-term payouts with a minimum payout length of 5 years for 183,000 retiring white-collar workers. I find that low accumulation of assets is strongly associated with the choice of the 5-year payout. Consistent with individuals selecting payout length based on private information about their mortality prospects, individuals who choose the 5-year payout are in worse health, exhibit higher ex-post mortality rates and have shorter-lived parents than annuitants. Individuals also seem to respond to large, tax-induced changes in annuity prices.            Essay III: This essay estimates the causal effect of postponing retirement on a wide range of health outcomes using Swedish administrative data on cause-specific mortality, hospitalizations and drug prescriptions. Exogenous variation in retirement timing comes from a reform which raised the age at which broad categories of Swedish local government workers were entitled to retire with full pension benefits from 63 to 65. The reform caused a remarkable shift in the retirement distribution of the affected workers, increasing the actual retirement age by more than 4.5 months. Instrumental variable estimation results show no effect of postponing retirement on the overall consumption of health care, nor on the risk of dying early. There is evidence, however, of a reduction in diabetes-related hospitalizations and in the consumption of drugs that treat anxiety. Essay IV (with Per Engström): The consumption based method to estimate underreporting among self-employed, introduced by Pissarides and Weber (1989), is one of the workhorses in the empirical literature on tax evasion/avoidance. We show that failure to account for transitory income fluctuations in current income may overestimate the degree of underreporting by around 40 percent. Previous studies typically use instrumental variable methods to address the issue. In contrast, our access to registry based longitudinal income measures allows a direct approach based on more permanent income measures. This also allows us to evaluate the performance of a list of instruments widely used in the previous literature. Our analysis shows that capital income is the most suitable instrument in our application, while education and housing related measures do not seem to satisfy the exclusion restrictions.

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Title: Annuity modelling in MTPL Author: Bc. Agáta Eštóková Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Karolína Kočová Supervisor's e-mail address: kkocova@koop.cz Abstract: This diploma thesis focuses on the possibilities of using generational mortality tables for third party liability insurance, mainly for bodily injured. It describes the construction of generational mortality tables and the creation of RBNS claims reserves. Besides the demonstration of these models, the work analyzes the results of calculating reserves in accordance with generational mortality tables and actual mortality tables of the Czech Republic. An impor- tant element in provision calculating is the simulation of future life expectancy of the insured, i.e. random generation of life expectancy based on generational mortality data. Characteristics of the distribution of reserves are derived from simulations. Furthermore, we compare the results of stochastic and determi- nistic approach of computing the reserves. Keywords: third party liability insurance, RBNS, annuity, generational morta- lity tables.

Motivated by the Guaranteed Minimum Death Benefits (GMDB) in variable annuities, we are interested in valuing equity-linked options whose expiry date is the time of the death of the policyholder. Because the time-until-death distribution can be approximated by linear combinations of exponential distributions or mixtures of Erlang distributions, the analysis can be reduced to the case where the time-until-death distribution is exponential or Erlang. We present two probability methods to price American options with an exponential expiry date. Both methods give the same results. An American option with Erlang expiry date can be seen as an extension of the exponential expiry date case. We calculate its price as the sum of the price of the corresponding European option and the early exercise premium. Because the optimal exercise boundary takes the form of a staircase, the pricing formula is a triple sum. We determine the optimal exercise boundary recursively by imposing the “smooth pasting” condition. The examples of the put option, the exchange option, and the maximum option are provided to illustrate how the methods work. Another issue related to variable annuities is the surrender behavior of the policyholders. To model this behavior, we suggest using barrier options. We generalize the reflection principle and use it to derive explicit formulas for outside barrier options, double barrier options with constant barriers, and double barrier options with time varying exponential barriers. Finally, we provide a method to approximate the distribution of the time-until-death random variable by combinations of exponential distributions or mixtures of Erlang distributions. Compared to directly fitting the distributions, my method has two advantages: 1) It is more robust to the initial guess. 2) It is more likely to obtain the global minimizer.

隨著醫藥科技的發達和公共衛生的進步，人類平均壽命不斷持續的延長， 致使我國將邁入高齡化的社會。又因小家庭制度的盛行，生活費用的增加 ，社會風氣的改變等因素，使得人們不得不為自己老年或退休後的生活預 作打算，而年金保險在此時即扮演對老年生活極佳之財務規劃工具。然而 ，壽險公司在推出年金保險商品之前，必須先要有一套年金生命表為計算 依據，本文除論述年金保險和年金生命表之概念外，亦介紹美、日兩國的 年金生命表及歷年之年金生命表，對年金生命表的編製更作一番詳細的探 討，並嚐試編製出一套適合我國目前情形的年金生命表，其各章摘要如下 ：第一章 係就研究動機、目的、範圍、限制、方法、內容及論文架構 加 @ 以說明。第二章 旨在說明年金、年金保險和退休金三者的 意義及範圍，並敘述三者之差別，同時亦介紹美、日兩國經營年金保險的 情形。第三章 旨在說明生命表的意義、種類和編製過程，並敘述年金生 命表的衍變及與壽險經驗生命表的差別和適用的險種，同時再介紹美、日 兩國的年金生命表。第四章 旨在說明可用於編製年金生命表的方法，及 目前適用我國的編製方案及其編製過程，並試編兩方案生命表死亡率，接 著說明影響年金生命表的因素及安全率的附加，最後介紹使用後調整死亡 率的方法。第五章 除了說明與年金生命表死亡率有關之保險費、責任準 備金、解約金、紅利和保險金之計算方式外，並設計電腦程式，用以計算 第四章編製完成之死亡率為基礎之純保費，並變動各項因素來探討其結果 ，及與其他金融業年金商品之競爭性。第六章 係就前述各章結果下總結 ，並就研究心得對壽險業及主管機關提出建議。

In Taiwan area, the mortality rates at all ages have decreased since the end of World War II, and the life expectancy of people has increased from 62 in 1950's to 75 in 2000, which is an increase of 21%. The mortality improvement of the elderly (i.e. people ages 65 and over) is especially significant, which effects in the rapid population aging in Taiwan area. For example, the proportion of the elderly has increased from 6.14%in 1990 to 8.52% in 2000. On one hand, the prolonged life span for an individual means a longer period of retirement life and thus a larger retirement fund. On the other hand, a longer life for the government is equivalent to a more thorough social system for the elderly. Therefore, a reliable mortality rates projection is essential to both personal financial and social welfare planning. 　　In this study, we have two main objectives: First, we explore some frequent used models, such as Lee-Carter, multivariate regression and principal component methods. We use the data between 1950 to 1995 as the pilot data and 1996 to 2000 as the test data to judge which method has the smallest prediction error. In addition, based on computer simulation, we also evaluate the performance of the estimation methods for the Lee-Carter method. The second part (and the other objective) of this study is to explore the effect of mortality improvement on the pure premium of annuity insurance. In particular, we calculate the pure premium of the annuity under the best model acquired from the first part, and compare those under 1989 TSO and other life tables. We found that the pure premiums under current life tables are under estimated, which may cause the insolvency of insurance companies.