We determine the optimal allocation of funds between the fixed and variable sub-accounts in a variable annuity with a GMDB (Guaranteed Minimum Death Benefit) clause featuring partial withdrawals by using a utility-based approach. In section two, the Merton method is applied by assuming that individuals allocate funds optimally in order to maximize the expected utility of lifetime consumption. It also reflects bequest motives by including the recipient's utility in terms of the policyholder's guaranteed death benefits. We derive the optimal transfer choice by the insured, and furthermore price the GMDB through maximizing the discounted expected utility of the policyholders and beneficiaries by investing dynamically in the fixed account and the variable fund and withdrawing optimally. In section three, we add fixed and stochastic income to the model and find that both human capital and the GMDB will influence the insured's allocation and withdrawal decisions. Section four explores the GMDB effects if there is also a term life policy available in the market. Our work suggests that if term life insurance is available and is continuously adjustable, fairly priced GMDBs may not be useful investments and the existence of GMDBs does not affect term life policy demand significantly.

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隨著高齡社會的來臨，必須考量面臨高齡化所帶來的種種衝擊和影響。台灣目前面臨嚴重的高齡化問題，我國早已於民國82年，正式邁入高齡化社會且於107年進入高齡社會。隨後將於115年進入超高齡社會。高齡化的速度逐漸超越日本、美國與歐洲等先進國家。 加上2017年推動的年金改革，廣大軍、公、教人員的所得替代率也將於十年內減少15%，面對接踵而來的老年退休安養問題，我們也開始思考除了政府未來會碰到社會福利支出將逐年增加以外，商業年金保險是否可以在這樣的環境變遷之下，提供即時且必要的幫助，進而於本研究中檢視保險年金的商品種類與銷售狀況，並就國內外的年金保險制度進行比較，試著找出國人不喜歡買年金的原因，並探討如果調整商品設計或政府提供怎樣的獎勵措施，會有助於年金保險的推展，進而讓年金保險在這樣的環境變化中扮演其更積極正面角色，凸顯其重要的社會價值。 透過文獻探討、實際數據的分析和比較及深度訪談，不斷地去釐清問題找出原因，並就其原因進行歸納整理，做成研究結論和建議方向。

We develop a stochastic control model for an investor's optimal investment and consumption over an uncertain planning horizon when the investor is endowed with a defaultable income stream. The distributions of the random time of default and the random terminal time are prescribed by deterministic hazard rates, and the investor makes investments in a standard financial market with a bond and a stock, modeled by geometric Brownian motion. In addition, the investor purchases insurance against both default and the terminal date, the default insurance serving as a proxy for the investor's disutility for default. We approximate the original continuous-time problem with a sequence of discrete-time Markov chain control problems by applying dynamic programming and the Markov chain approximation. We demonstrate how the problem can be solved numerically through a logarithmic transformation of the investor's wealth variable, even when the utilities are CRRA with large risk aversion parameter. The model and computational approach are applied to a retiree's optimal annuity decision in the presence of default risk, and we demonstrate that default risk can lead a retiree to annuitize significantly smaller proportions of savings, even when a portion of the defaulted annuity can be recovered, than is traditionally considered optimal by the retirement-finance community. Hence, we show that credit risk may play an important role in resolving the annuity puzzle.

The purpose of this study is to investigate the pricing of variable annuity embedded derivatives in a Lévy process setting. This is one of the practical issues that continues to face life insurers in the management of derivatives embedded within these products. It also addresses how such providers can protect themselves against adverse scenarios through a hedging framework built from the pricing framework. The aim is to comparatively consider the price differentials of a life insurer that prices its variable annuity guarantees under the more actuarially accepted regime-switching framework versus the use of a Lévy framework. The framework should address the inadequacies of conventional deterministic pricing approaches used by life insurers given the increasing complexity of the option-like products sold. The study applies finance models in the insurance context given the similarities in payoff structure of the products offered while taking into account the differences that may exist. The underlying Lévy process used in this study is the Variance-Gamma (VG) process. This process is useful in option pricing given its ability to model higher moments, skewness and kurtosis, and also incorporate stochastic volatility. The research results compare well with the regime-switching framework besides the added merit in the use of a more refined model for the underlying that captures most of the observed market dynamics. / Dissertation (MSc)--University of Pretoria, 2014. / tm2015 / Mathematics and Applied Mathematics / MSc / Unrestricted

In this thesis we deal with the longevity risk originating from the uncertain future evolution of mortality at adult-old ages. It may emerge in particular because of an unanticipated reduction in mortality rates. That risk is significant for annuity and pension providers. We consider a model portfolio represented by one cohort of recipients of immediate life annuities. We introduce possibilities for assessing the risk of such portfolio. A comparison of the impact of longevity risk is made with random deviations in mortality rates. We also deal with the question of solvency of the insurer by investigating the solvency capital requirement for longevity risk.

台灣逐漸步入高齡化社會，由於各種經濟社會因素，一般個人利用早年的儲蓄準備退休後的生活，已是不可避免的趨勢。衡諸個人自己獨力負擔退休生活所需的準備，不外乎是加入保險，藉助集體互助的力量達成，或是自力儲蓄，藉由金融工具的使用，累積財富。在政府宣示的亞太營運中心計劃勢必將帶動國內金融發展。屆時，行之歐美諸國已久的遞延年金商品可望引進台灣的保險業界，使自力儲蓄的個人能透過金融商品的多元化，選擇最有效用的金融商品，以謀取退休後的生活準備。鑑於美國業者經營遞延年金商品的教訓，在文獻的閱讀之中，筆者發現利率風險在精算界所受到的重視與發展成果值得國人借鏡，因此發奮研究利率風險在遞延年金商品中所扮演的角色，份量及其因應之道。希冀能在未來國內業者推行遞延年金之際，對經營此商品所面臨的風險能有清楚的認識，也希望監理機關能了解業者的需求而給予適度的協助。相信在健康的經營環境下，遞延年金商品會替消費者帶來莫大的福祉。本論文的研究方法為文獻探討，研究方向與目的有三：一、了解遞延年金商品的內容及其使用價值。二、辨識遞延年金商品的利率風險。三、探討如何衡量遞延年金商品利率風險與其管理的方法。 / When Taiwan stepped into old-aged society, as driven by variety of economic and social forces, an individual has to prepare for his(her) retirement during the ealier working years. By doing so, he(she) can enter into the insurance plans or mutual help-each-other societies, or by individual self-saving plans and use of new financial instruments. Now, the Taiwan Government initiate an Asian Operation Center Project that may have the domestic financial market boomed up. By that time, it's possible that Deffered annuity products sold in foreign countries like USA or those in Europe over many years will appear at Taiwan market and bring the Taiwan consumer more efficient ways of preparation for retirement. After the inspection of lessons learned by United States life insurance companies while these company were selling the Defferd Annuities, the author find that the interest rate risk are emphasized extensively in actuarial literatures and it's development is worth while the domestic companies to take lessons. Thus, the author study the problem with interest rate risk and the proper measures to manage the risk. It's hoped that in the coming future, at the time of Deffered Annuities, the domestic companies will already have clear understandings about the risks they face. And it's hoped that the government understand the insurance companies' needs and give them help. It's believed that in a sound environment, the consumer will benefit from the advent of Deffered Annuities. The research method used is literature research, and the direction and goal of the study is as follows: 1.Understand what's Deffered Annuity and it's uses. 2.Indentify the interest rate risks inherent in Deffered Annuities. 3.Examine the various measures to manage the interest rate risk.

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Thesis advisor: Peter Ireland / Retirees with limited financial resources face numerous risks, including out-living their money (longevity risk), investment losses (market risk), unexpected health expenses (health risk), the unforeseen needs of family members (family risk), and even retirement benefit cuts (policy risk). This study systematically values and ranks the financial impacts of these risks from both the objective and subjective perspectives and then compares them to show the gaps between retirees’ actual risks and their perceptions of the risks in a unified framework. It finds that 1) under the empirical analysis, the greatest risk is longevity risk, followed by health risk; 2) under the subjective analysis, retirees perceive market risk as the highest-ranking risk due to their exaggeration of market volatility; and 3) the longevity risk and health risk are valued less in the subjective ranking than in the objective ranking, because retirees underestimate their life spans and their health costs in late life. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

The purpose of this study is to collect, organize, and present information pertaining to the development of teacher retirement systems in the United States, with special emphasis upon the benefits and services such systems can render to the thousands and thousands of teachers who have given their lives to the cause of teaching the youth of America.